Preheat grill pan on stovetop over medium-high heat. Cook patties 5 to 6 minutes per side or until no longer pink. Top with cheese, and let stand 1 minute or until melted.
Stir together mayonnaise and vinegar. Spread mayonnaise mixture on buns. Serve burgers on buns with basil and tomatoes.
Side Dish Directions
Preheat oven to 450°F. Spread pineapple in a single layer on a rimmed baking sheet. Drizzle with lime juice.
Bake 15 minutes or until pineapple is beginning to brown.