In a medium bowl, stir together tuna, cannellini beans, red onion, mayonnaise, and garlic. Set aside.

Preheat an electric sandwich press, a covered indoor grill, a grill pan, or a skillet. To assemble sandwiches, spread half of the bread slices with the tuna mixture. Top tuna mixture with tomato slices, basil leaves, and cheese. Top with remaining bread slices. Coat outside of each sandwich with nonstick cooking spray.

Place sandwiches (half at a time, if necessary) in the sandwich press or indoor grill; cover and and cook about 6 minutes or until cheese melts and bread is toasted. (If using a grill pan or skillet, place sandwiches on grill pan. Weight sandwiches down with a heavy skillet and grill about 2 minutes or until bread is toasted. Turn sandwiches over, weight down, and grill about 2 minutes more or until remaining sides of bread are toasted.)