2 roasted red bell peppers (from a jar), each cut in half
In a medium skillet over medium heat, warm the oil. Add the onion and garlic and sauté until tender, about 5 minutes, stirring occasionally. Remove from the heat and let cool for at least 5 minutes. Combine the onion and garlic with the remaining patty ingredients, and then gently form four patties of equal size, each about 1 inch thick. With your thumb or the back of a spoon, make a shallow indentation about 1 inch wide in the center of the patties to prevent them from forming a dome as they cook. Refrigerate the patties until ready to grill.
Prepare the grill for direct cooking over medium heat (350° to 450°F).
Brush the patties on both sides with oil, and then grill over direct medium heat, with the lid closed, until fully cooked (165°F), 11 to 13 minutes, turning once. During the last 30 seconds to 1 minute of grilling time, toast the buns, cut side down, over direct heat.
Build each burger on a bun with mayonnaise, a lettuce leaf, a roasted bell pepper half, and a patty. Serve immediately.