Combine the first 4 ingredients in a bowl and refrigerate.
Preheat your grill to medium-high. Brush the peppers with oil, grill 1 minute per side, and then remove.
Grill the burgers 4 minutes per side, or until entirely cooked through. Top burgers with 2 slices of cheese and cook 1 minute more. Spread the buns with the chili mayo. Top the bottom buns with lettuce. Set on the burgers, peppers, tomatoes and top buns, and serve.