In a skillet, cook the bacon over moderate heat until crisp, 6 minutes; drain on paper towels. In a bowl, mix the 1/2 cup of mayonnaise with the garlic; season with salt and pepper.
Brush the cut sides of the rolls with 2 tablespoons of the oil and lightly toast on the grill. Brush the burgers with the remaining oil and season well with salt and pepper. Grill over moderately high heat for 3 minutes; flip and top with the cheese. Cook for 3 more minutes for medium-rare. Spread the bottom roll halves with the garlic mayonnaise. Top with a burger, bacon, avocado, lettuce and onion and serve.