Heat a skillet over medium heat and add a splash of extra virgin olive oil. Sauté the chopped medium yellow onion and diced white button mushrooms for 10-15 minutes until they become soft and caramelized. Season with a pinch of salt and pepper. Remove from heat and set aside to cool.

In a large mixing bowl, combine the lean ground beef with your chosen BBQ seasoning. Mix gently with clean hands, being cautious not to overmix.

Form the ground beef mixture into ½-pound patties and make a slight indent in the center of each patty for the filling. Spoon in the sautéed onions and mushrooms, add a slice of cheddar cheese, and seal with more beef on top.

Preheat your grill to medium heat. Place the stuffed burgers on the grill and cook for approximately 6 minutes on one side, then flip and cook for an additional 6 minutes.

Once grilled to perfection, transfer the burgers onto buns and customize with toppings like lettuce and tomatoes. Serve immediately.