Not an expert - but the recipes I have seen always include flour. Otherwise I am afraid you will have a big lumpy mess on your hands.
Cook veggies in small amount of butter - remove veggies and set aside - reserve the liquids.
To the liquids, add flour and chicken stock - heat til thickened.
Add the veggies,the beer and the cheese(grated) - cook all about 20 minutes or so.
There’s a cheese soup in the Lowfat Moosewood Cookbook that has no flour; it relies on potatoes instead, but yes, you definitely need some starch to keep the cheese from getting globby.
If anyone’s interested in that recipe, I can post it later, but while it’s awesome, it’s all good for you and stuff, so it’s not the sort of thing the OP’s looking for, I’m pretty sure.
blah! I did the saute part with onions and such, and I’ve totally run out of steam. Now I don’t feel like I have the energy to finish. I guess I’d rather be the type to have soup served to me than the maker of soup.
Dunno about the beer, but Alton Brown made a yummy-looking cheese soup in an episode of Good Eats, that heavy-handedly goofy food programme that redeems itself through the quality of its recipes and its scientific, pragmatic approach to cooking. (Could somebody please inform Alton that in this universe the correct pronunciation of “Worcestershire” is not “wishter-sheer”?)