Olive oil for coating
1 package turkey breast
4 slices mozzarella cheese
1 small bunch fresh basil leaves
Salt and freshly ground pepper
1/4 cup salted butter, at room temperature
1 large clove garlic, minced
1/8 teaspoon cayenne pepper
Prepare your gas or charcoal grill for medium-high direct heat grilling. Oil the grill rack.
Butterfly the turkey breasts using a long, thin, sharp knife: cut each turkey tenderloin horizontally into the thickest part, to within 1/2-inch of the other side (so that it can be opened like a book) then cut each in two. Do the following with each breast: Open the tenderloin like a book and place between sheets of plastic wrap. Pound lightly, using a meat mallet, to even out the thickness. Remove the top sheet of wrap. Place 1 slice of cheese and a few basil leaves on one half of the breast. Sprinkle with salt and pepper and close the breast. Coat with a little olive oil, and sprinkle both sides with salt and pepper.
In a small bowl, combine the remaining 3 ingredients with a fork and mix well. Form into a log in waxed paper and refrigerate until ready for use. Grill turkey breasts for 3 to 5 minutes on each side, or until no longer pink in the center. Top each breast with a pat of the garlic butter.