Thinly slice the yellow onion into even rounds.
Heat the olive oil in a small skillet over medium-low heat and add the sliced onions.
Cook the onions slowly, stirring occasionally, until they are soft and deeply golden brown, about 15 minutes.
In a medium bowl, gently combine the ground beef with smoked paprika, sea salt, and black pepper.
Shape the beef mixture into one large patty, being careful not to overwork the meat.
Preheat a grill or cast-iron skillet to medium-high heat.
Grill the patty for 4 to 5 minutes per side or until it reaches your desired level of doneness.
Place the burger bun cut-side down on the grill for the last 60 seconds to lightly toast.
Assemble the burger by placing the patty on the bottom bun and topping it with the caramelized onions, lettuce, tomato, and mustard.