Preheat the grill to 240°C (464°F, high heat). Cut the red onions into rings. Grate the Manchego and cheddar cheese. Cut the tomatoes into slices. Wash the lettuce. Mix equal parts ketchup, mustard, and barbecue sauce in a bowl to make the burger sauce.
Grind the beef (or use pre-ground beef). Season with salt and pepper and mix well. Divide into 4 equal portions of roughly 200g each. Using wet hands or a meat press, form each portion into a flat patty about 1 cm thick with a shallow indent in the center—this prevents the patty from puffing up while cooking.
Place the burger patties on the grill and cook the first side for 4 minutes on high heat. Flip and cook the second side for 2 minutes. Transfer to a plate and top each patty with onion rings and cheese. Place bacon strips on the grill and cook for 5-7 minutes until crispy. Toast the cut sides of the burger buns on the grill for 1-2 minutes until lightly browned.
Brush the inside of each bottom bun with burger sauce. Layer with lettuce, tomato slices, the cheese-topped beef patty, and bacon. Cover with the top bun and serve.