So many good options for melty cheese including Gruyère, muenster, Monterey jack, and provolone. Use two to three ounces of cheese, by weight, per sandwich depending on how much cheese you like in your grilled cheese. You have the option to either use grated cheese or sliced cheese. With grated, you will mix the cheese and the melted squash together before putting into the sandwich. With sliced, you’ll simply layer the melted squash between slices of cheese.