Not at all - I’m horribly allergic to tomatoes and also to many legumes (beans) yet I’d love to have a vegetarian stock recipe I could use. So I’m waiting with baited breath for a response as well.
You must learn to curve the path of the vegetables as they are thrown into the pot. We, the ancient order of stew chefs, have developed special veggie projectiles which will help you curve the flightpath of your produce.
Take one large vegetarian…
Find a ratatouille recipe on a website like epicurious.com and modify it to suit your taste.
Not so much a recipe as a suggestion for a savory base that doesn’t use tomatoes or meat. Mushroom stock is hearty and tasty and has umami. Soaking dry shrooms makes a good stock (I would receommend morels, for instance), then it’s just a question stewing some selected veggies in it and thickening it with flour.
ETA you can also buy mushroom boullion.
I made this up as a cross between ratatouille (but simpler) and pasta sauce and and cooked it today. I included a small handful of smoked bacon and some anchovies but you can leave them out and add a bit of salt and possibly some cloves instead - they’re really just there for taste.
Chop up finely:
1 onion
1 clove of garlic
1 smallish carrot
Chop up into big chunks:
1 can of peeled tomatoes (about 400 grams or so) or use chopped canned tomatoes.
1 large courgette
2 large “peppers” - I haven’t been able to find out what these things are; my local Turkish grocery shop sells them. They look like giant green Spanish peppers (long and pointy, about 20 cm long). Like this. And they’re hotter and less bitter than bell peppers but not nearly as hot as Spanish peppers. You can probably replace them with a red or green bell pepper and one or more hot peppers to taste.
Also needed: olive oil for frying and about a glass or two of red wine.
Heat up the oil in a large frying pot (I use a cast iron pot, but any kind of deep pot is fine).
Add the onion, garlic & carrot. Fry while stirring occasionally on a fairly low heat until it starts to stick or the onion is soft. Add the courgette and fry a little longer (a minute or 3).
Then add the tomatoes and enough wine to almost cover. Heat to the boil, turn down the heat to very low and leave to bubble softly for half an hour. Stir occasionally.
If you are using the bacon and anchovies, add the anchovies to the oil first on a very low heat. Then add the bacon with the onion etc.
If not, you’ll probably want to add one or two cloves with the onion and season with salt near the end of cooking (no salt is needed if you use anchovies and bacon). Or replace some of the wine with vegetable stock. Or add soaked dried Chinese mushrooms and their soaking water.
Serve with rice or couscous. Drink the rest of the wine.
If you’re willing to spend some extra time at the stove, I guess frying the courgette separately in some oil and only adding it when plating will improve the taste (like it does for ratatouille). I was too lazy to try that today.
Also add the peppers here.
I just want to add that slow cookers are really mostly useful for stewing meat. Most vegetables are about as done as they will get within half an hour even on low heat, with a few exception like potatoes, rice and lentils which are usually better off cooked on fairly high heat in steam or lots of water.
Other veggies usually don’t improve from cooking until falling apart, but some cuts of beef and lamb definitely do. Of course, if you’re combining lamb neck and lentils, then fine; it’s going to take forever anyway. But if you’re doing plain veggies, you’re really much better off cooking your potatoes etc separately. It’ll take an age to slow cook potatoes, and all you’ll end up with is boiled potatoes.
I’m sure the result is lovely, but I’m puzzled why, when the OP have firmly stated no meat and no tomatoes, you offer a recipe with fish, pork, and tomatoes in it.
I do agree, however, that mushrooms can make lovely stock. My favorites for that are dried shiitake mushrooms, but others will work, too.
I make a light broth or dashi (that’s Japanese, if I spelled it right) using dried shiitakes and kombu, a type of dried kelp, that I steep much like tea for about 20 minutes. But while that makes a tasty soup it’s not thick enough for what I’d call stew.
As I stated fairly clearly at the beginning of that post, the fish and bacon are minimal and are just there to strengthen the taste - this is not a “fish and pork” recipe - and I noted very simple (and I think effective) replacements in that same post. Though now that I think of it, I’d add some mace or nutmeg too.
The OP came out later with the the no-tomato rule. Didn’t spot that at first. Can’t think of any decent replacement. Replacing the tomato with stock and then thickening out the sauce at the end with corn/potato starch might work, but I’d really have to try that before I’d recommend it.
Sorry.
I made this Tanzanian Veggie Soup a couple of weeks ago. It easily thickens to a stew like consistency if you’re heavy-handed with the peanut butter and you use the right potatoes. It has some chopped tomato, but you could easily leave that out and it shouldn’t throw off the taste. It’s a wonderful recipe.
I must cook too often for people with serious food allergies and severe chronic medical problems - for them, ANY amount of a forbidden substance is too much. I have a niece who can wind up in the hospital merely by entering a kitchen where fish is being cooked. For me, merely touching tomato juice can give me a rash like poison ivy, I really don’t want to eat it in any amount. Friends who once added “just a tablespoon” of ketchup to 4 quarts of stew that they served me for dinner, despite my warnings about how sensitive I am, resulting in a call to 911 and several hours in the ER for me, not to mention nearly a month of medication and recovery time. Pardon me if my history has made me over-sensitive. Just, please, do be aware that there is a difference between those who can tolerate some of something, and those who can tolerate none. I wouldn’t want you to inadvertently cause someone harm when your intention was merely to “strengthen” a pot of stock.
Yeah yeah yeah. Next time, read further than the first part of the first sentence.
I was fairly mystified as well; however, even if I’ll never make this particular recipe*, maybe someone else in the thread will enjoy it, so it’s all good. 
- To me a recipe that requires fish and bacon to have good flavour isn’t vegetarian so I would never try to mimic the taste of bacon, in particular with other items - I just wouldn’t make it.