Preheat grill to medium-high heat.
Mix together mayonnaise and 1 teaspoon of Cajun seasoning. Set aside.
Mix ground sirloin, jalapeno pepper, onion, garlic, 1 tablespoon Cajun seasoning, and Worcestershire sauce. Use your hands to blend thoroughly.Divide into 4 balls, and flatten into patties.
Lightly oil the grill, and place the patties on it. Cook for about 5 minutes per side for a well-done burger. Melt a slice of cheese on top of each patty by placing it on the patty after about 3 minutes.
Spread the seasoned mayonnaise on the buns. Assemble the burgers with lettuce and tomato on top.
If I have good hamburger buns (I like Sara Lee Egg hamburger buns with sesame seeds) you might like to toast them on the grill before applying the mayonnaise.