Apply butter or mayo to one side of the bread. Flip it over and apply butter or mayo to the other side. Lay it on a plate. Lay the cheese on top of the bread. Apply butter and mayo in the same way on the second slice of bread. Lay it on top to complete the sandwich. Repeat to assemble all sandwiches.
Heat your grill or frying pan to medium-low. You can raise the temperature to medium if your cheese is melting rapidly enough.
Place the sandwiches in the pan. Grill until lightly browned and flip over. Continue grilling until cheese is melted and bread is browned on the second side. Press down with a spatula to get a crispy panini bread crust.