Combine beef, jalapenos, garlic, cayenne pepper and eggs in a mixing bowl.
Sprinkle generously with hot sauce and mix in.
Preheat the grill to medium heat for 10 minutes.
Form beef mixture into burgers and place into open burger basket. Lock basket and place on grill for about 5 minutes. Flip and keep on grill for another 5 minutes to desired meat temperature.
Remove from basket and place burgers on buns adding pepper jack cheese.