Prepare gas grill for medium-high to high heat and let warm up during preparation.
Mix the ground chuck with the Worcestershire, liquid smoke, 2 tablespoons of the hot sauce, red pepper, eggs, jalapenos and garlic until everything is mixed well. Then form into six equal size balls and pat into patties until they are about one inch thick. Make an indentation in the center of each patty to help prevent swelling in the center. Brush or spray one side of each patty with the olive oil and then sprinkle the Cajun seasoning on each burger (you will do the other side after you have placed the burgers on the grill).
Place patties on the grill, seasoning side down, and let grill for 4 minutes with cover down. Open cover, spray or brush the olive oil on the uncooked side of the patties, sprinkle with the Cajun seasoning and flip the burger. Let cook again for 4-5 minutes (for a medium to medium well done burger).
While the burgers are cooking, brush rolls with melted butter and then mix the remaining butter with the 4 tablespoons of hot sauce.
During the last minute of cooking, place equal amounts of bleu cheese on each patty, then place the rolls, buttered side down, over the flame and let toast for 30 seconds to one minute. Lower the cover one last time to help melt the bleu cheese.
Remove rolls first, then place patties on the bottom portion of the toasted buns. Brush top of the rolls with the hot sauce/butter mixture, then top with your favorite toppings and serve.