Season the beef with the cayenne, garlic powder and oregano in a medium bowl. Form the beef mixture into 4 patties. Divide each patty, through the center, into 2, and flatten. Place the blue cheese on 1 patty and top with the other patty. Pinch the edges to seal. Grill burgers in a cast-iron pan or on a grill over medium-high heat to desired degree of doneness. Serve on the hamburger buns.