Brush top side of each bread slice with melted butter. Flip 4 slices over, sprinkle with cheese and compact lightly with hand. Cover with remaining bread slices, buttered side up.
Heat large nonstick skillet or griddle over medium-low heat for 1 minute.
Place 2 sandwiches in pan on the griddle. Weight them down with a round cake pan, pressing lightly. Leave cake pan on top and cook until first side is golden brown, about 3 to 5 minutes. Flip sandwiches, press again with cake pan and cook until golden brown, about 2 minutes.
Repeat with remaining sandwiches.
Variations: Add one very thin slice of red onion, rings separated, while filling sandwiches. Or, add slices of very thinly sliced salami.