Which type of cheese is the best for a grilled cheese & tomato sandwich?

Grilled cheese & tomato sandwiches are an American staple after all. Ideally, I would prefer to use mozzarella, but it's difficult to find mozzarella cut to the exact proportions of a slice of bread. And most mozarella is sliced too thick for toasting. Too bad because mozarella goes great on a GC&T, with a... show more Grilled cheese & tomato sandwiches are an American staple after all.

Ideally, I would prefer to use mozzarella, but it's difficult to find mozzarella cut to the exact proportions of a slice of bread. And most mozarella is sliced too thick for toasting. Too bad because mozarella goes great on a GC&T, with a little basil and olive oil.

I've tried using Swiss but it just doesn't have the right taste.

American is too cheap. Cheddar is a possibility but seems to have too strong of a flavor for a GC&T.
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