1 medium sweet onion, sliced crosswise into 1/4-inch-thick rings
1 1/2 pounds ground beef chuck
4 slices smoked cheddar cheese (about 4 ounces)
4 burger buns with sesame seeds, split
1/2 cup barbeque sauce
In a large skillet, cook the bacon over moderately high heat until crisp. Drain on paper towels.
In a medium saucepan, heat 2 inches of oil to 350°. In a shallow bowl, combine the flour with the cayenne and season generously with salt and pepper. In another shallow bowl, whisk the buttermilk with a generous pinch each of salt and pepper.
Working in batches, dredge the onion rings in the seasoned flour. Dip the rings in the buttermilk, allowing the excess to drip off, then dredge again in the flour. Fry the rings until golden brown and crisp, about 2 minutes per batch. Drain on paper towels and season with salt.
Meanwhile, heat a cast-iron griddle or grill pan. Form the ground meat into 4 patties about 3/4 inch thick and make a depression in the center of each one with your thumb. Brush the burgers with oil and season generously with salt and pepper. Cook over moderately high heat until well browned on the bottom, about 4 minutes. Flip the burgers and cook for 2 minutes longer. Top each burger with a slice of cheese and tent with foil. Cook for 2 minutes longer, until the cheese is slightly melted and the burgers are medium rare.
Set the burgers on the buns and top with the barbeque sauce, bacon and fried onion rings. Close the burgers and serve right away.