Thinly slice the yellow onion into half-moons.
Heat the olive oil in a small non-stick skillet over medium-low heat; add the onions and a pinch of salt, cooking for 15-20 minutes until soft and golden brown.
In a medium bowl, gently combine the ground beef with the smoked paprika, garlic powder, sea salt, and black pepper, being careful not to overwork the meat.
Form the beef into a single large patty, making it slightly wider than the bun to account for shrinkage.
Preheat a grill or cast-iron grill pan to medium-high heat and lightly coat with oil spray.
Grill the patty for 4-5 minutes per side for medium doneness, placing the cheddar cheese slice on top during the final minute of cooking to melt.
Place the whole wheat bun halves on the grill for 30 seconds until lightly toasted.
Assemble the burger by placing the butter lettuce and tomato on the bottom bun, followed by the cheesy beef patty and a generous heap of caramelized onions.
Top with the remaining bun half and serve immediately.