Most of my sandwiches don’t have cheese, but in keeping with your rules, two that do are a couple of prepared subs from the local deli. My fave is a roast beef sub on something that looks like a hoagie roll (the same kind of bread that Philadelphia cheesesteak sandwiches are usually made from), which has slices of white cheese (possibly white cheddar) to which I add sliced sauteed mushrooms and sauteed white onion and heat in the microwave, then add Dijon mustard. Definitely not toasted – I love how the microwaving not only heats up the roast beef and other ingredients and melts the cheese, and also softens the bread roll.
The other is the same type of sub but thickly piled with smoked turkey and the same cheese, and consumed cold. It already has lettuce but I’ll add sliced tomato and mayo and, if the mood strikes, a few rings of raw red onion.
Two come to mind, but I’ll only name one, lest I break some OP rule by naming multiple favorites:
A Philadelphia roast pork sandwich: slices of roast pork (dripping in jus), broccoli rabe, aged provolone (this is very important), long hots (peppers), on an sesame hoagie roll.
A very good Philly cheesesteak, or as I like them, a pizza steak. It needs to be on a quality Italian roll with thinly shaved ribeye, pizza sauce and melted provolone or mozzarella. No cheese sauce for me. Growing up, pizza steaks were very common on menus. Now, some places either don’t have them on the menu, or the sauce needs to be specified. We have a place we like that offers probably 8 different sauces/condiments, but they don’t offer pizza sauce.
Since I can add condiments I must add just the right amount of pizza sauce, not too much to make the bread soggy, it’s a fine balance. Also, I prefer a meatball mix of beef and sausage, my local Buschs market makes the perfect meatballs and sauce for this purpose.
A New Orleans muffuletta is a fantastic sandwich, but violates the OP’s conditions by having multiple meats and cheeses. My simplified home variation, however, fits the thread’s conditions and is my favorite meat/cheese/bread combo.
Instead of the traditional sesame-seeded muffuletta loaf, I prefer to use a palm-sized focaccia roll. Focaccia rolls used to be easy to find at our local groceries, but have been harder to source since the late-1990s. Still, there are a good number of local bakeries who offer them.
The meat and cheese are simple, and available at any local grocery: Chisesi boiled ham (local brand) and sliced mozzarella.
Since condiments are allowed, I’ll tap the only one this sandwich requires – olive salad, which is essentially de rigeur for any muffuletta, home version or not. Basically a distant cousin to @AHunter3’s olive tapanade detailed above. There are many brands of olive salad sold in local groceries.
The ONLY sandwich on which I combine both meat and cheese would be a braunsweiger and cheese sandwich. I’m indifferent to the type of bread used, although most typically it is whole wheat. Next choice would be a rye or pumpernickel. The addition of mustard as a condiment is optional. Otherwise I don’t mix meat and cheese.
Tricky. Does Reuben count if I condition it on sauerkraut and thousand island, served hot?
Or is the sandwich to stand on the three alone? How far can we take condiments?
I’ve been in an English muffin kick lately so I’ll go toasted EM, sausage patty, American cheese. Egg &mayo, if allowed.
Picking within the parameters @Czarcasm has set out, I’m going to take my current favorite sandwich, jambon beurre, and modify it slightly: an excellent baguette, quality ham, and a soft cheese like camembert.
Ah missed that follow-up. Mmm. Mine can be disqualified because of the broccoli rabe, unless it can be counted as a condiment. Is the pepper a condiment? If so, then just leave off the broccoli rabe. If not. Ugh. I don’t think I have a favorite that is just one meat, one cheese, one bread, and nothing else except for mustard or mayo. Maybe a simple hamburger, sesame bun, with blue cheese.