Combine the ground beef, basil, garlic, salt and pepper. Mix lightly and form into 4 equal patties 3/4-inch thick.
Grill over medium-hot coals to 160°F internal temperature.
Meanwhile, combine mayonnaise and prepared pesto sauce and set aside.
Cut focaccia bread into 4 pieces and split each in half horizontally. Spread each cut side of the bread with 1 Tbsp. of the mayonnaise/pesto mixture.
Top each hamburger patty with a slice of cheese during the last minute of grilling. Top with one fourth of the roasted red peppers and serve on the prepared focaccia bread.
