What cheese might compliment New England clam chowder? [closed]

I have recently become enamored of breadbowls. Not the San Francisco sourdough bowls that they serve on the Wharf; I like to make a basic French or pizza dough and form it over inverted bowls, cover with another bowl, fill the tins with beans and bake in 400°F oven, removing the top bowl after about 10 minutes to let inside crust brown a bit.

I made creamy minestrone the other night, then lined the bottom of one of my bowls with a slice of provolone, heated it in the oven until the cheese was just starting to bubble, then I removed it to let the cheese set a bit. The cheese helped prevent the soup from soaking through, and it was delicious as well.

So, my question: I’d like to do the same thing with a New England clam chowder, but what kind of cheese would compliment the chowder? I was thinking maybe Monterey Jack might be mild enough.