Preheat a non-stick skillet or griddle over medium heat.
Spread 2 tablespoons softened butter on one side of each of the 2 slices of sourdough bread.
If using, spread 1 tablespoon mayonnaise on the opposite side of 1 slice of bread.
Place 1 slice of bread in the skillet, buttered side down.
Layer 1 slice sharp cheddar cheese, 1 slice provolone cheese, and 1 slice mozzarella cheese on top of the bread.
Add the remaining 1 slice sharp cheddar cheese and 1 slice provolone cheese on top of the mozzarella.
Top with the second slice of sourdough bread, buttered side facing up.
Cook for 4–5 minutes, or until the bottom slice is golden brown and the cheese begins to melt.
Carefully flip the sandwich and cook for an additional 4–5 minutes, or until the second side is golden brown and the cheese is completely melted.
Remove the sandwich from the skillet and let it rest for 1 minute.
Slice in half and serve immediately.
Notes
Cooking Temperature: The cooking time is based on a medium heat setting. Monitor the heat closely while cooking, as cooking on too high of a temperature could cause the bread to brown too quickly without melting the cheese.