Using a food processor, chop the garlic. Add the basil and pine nuts and, with the machine on, pour in 1/2 cup olive oil and process until almost smooth.
In a medium skillet, heat 1/4 cup olive oil over medium heat. Add the onion and cook, stirring occasionally, until softened and browned, 15 minutes.
Meanwhile, preheat a grill or grill pan to high. In a medium bowl, combine the beef, crushed red pepper and 1 teaspoon salt. Shape into 4 patties; brush with the remaining 1 tablespoon olive oil, then grill for 5 minutes. Flip and grill for another 5 minutes; top with the cheese for the last 3 minutes of cooking. Grill the rolls until golden.
Spread the pesto on the roll bottoms; top each with a beef patty and some onions and cover with a roll top.