Preheat your barbecue or indoor grill to medium-high heat. Combine the mayonnaise with Tabasco sauce to taste, and then reserve in the fridge. Season the burgers with salt and pepper, and then grill until entirely cooked through, about 3-4 minutes per side. Top with cheese and allow it to melt. Spread burger buns with mayonnaise. Set a lettuce leaf on the bottom buns. Set on the burgers. Top the burgers with avocado slices and salsa and serve.