like mozzarella or Monterey Jack or a combo of the two...a Colby jack would give you the cheddar taste and color if that’s important. Pepper jack? Yum...

Because there is a recommendation I can give that would work, but, well let's have wiki explain:

Provel is a white processed cheese product particularly popular in St. Louis cuisine, that is a combination of cheddar, Swiss, and provolone cheeses. Provel has a low melting point, and therefore has a gooey and almost buttery texture at room temperature. It is the traditional topping for St. Louis-style pizza

I don't like the term "Processed cheese" in this case - Makes it seem like American Cheese singles or velveeta.

Provel is more of a blended cheese that is pushed through an extruder so it looks like thick noodles.

If you can find it, it would work like a champ in soups.

There is a bar and grill we go to that makes a beer cheese and spinach soup that I will fight people over

Sounds awesome. I may order some for fun. thanks.

Not sure why St Louis adopted this blend but its every where

I have to add a splash of milk. Worth it for the flavor in anything Cheeseburger!

Monterey Jack also a good melter.

Same with Mozzarella and gruyère

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The so-called "real" cheese and "real" dairy advertising effort has been do demonize the processed cheese market by suggesting those ingredients aren't "real". The reality is they contain the same basic ingredients as so-called "real" cheese minus the ground up animal organ meats along with some stabilizers that come in handy for the application you describe.

The reason why melting so-called "real" cheese into liquid ingredients becomes a problem is because it wants to separate into the constituent solids, liquids, and fats. So instead of creamy cheesy goodness you get a gooey mess that doesn't incorporate.

The good news is there is an answer and that answer is to turn "real" cheese into processed cheese yourself by shredding it and applying a light coating of corn starch. Add this to your hot soup a small handful at a time and make sure each addition melts before adding the next. It also helps to use better melting cheeses that have a higher fat content and are semi-firm. So if it has the consistency of gouda, then it probably is a good melting cheese. Softer and harder cheeses aren't as good for this application.