Divide the sausage into 4 equal portions and form each one into a thin patty. Make a slight indentation in the center to prevent shrinkage.
Heat a skillet over medium-high heat or preheat an outdoor grill for a medium-hot fire. Cook the patties on the hot skillet or grill over direct heat until cooked through, 5 to 7 minutes.
Meanwhile, in a medium skillet, heat the oil over medium-high heat and cook the onion and peppers until very soft and starting to brown, about 7 minutes. Season with salt and pepper.
In a small bowl, combine the mayonnaise, basil, oregano, and garlic. Stir well.
To assemble the burgers, place one burger on a bottom bun half. Layer on the tomatoes, lettuce, and sauce, and top the bun.
Make-ahead: The patties can be formed and the mayonnaise spread can be made up to 1 day in advance and stored in the refrigerator until ready to cook the burgers.
Notes
Nutritional values are approximate and are based on ¼ of the recipe. Refrigerate leftovers promptly and use within 4 days.