Split the focaccia. Prepare the basil butter by combining soft butter and basil in a food processor.
Assemble the panini with even layers of basil butter, prosciutto, roasted red tomatoes, fresh mozzarella, and top with the second slice of buttered focaccia.
Toast the sandwich on a panini press and cut into pieces as desired.
These sandwiches can be prepared up to 8 hours in advance and stored in the refrigerator until pressing.