Grate the onion on the fine holes of a grater. Run a knife through the onion after you are done grating. Place the onion in a bowl with the ground turkey, Worcestershire sauce, bbq sauce, olive oil, sea salt and black pepper. Mix together well with your hands.
Shape into four patties and press the patties into ½-inch thick rounds. The mixture will be quite moist. Prep all the toppings of your choice and place on a plate.
Heat 1/2 tbsp olive oil in a nonstick griddle or large nonstick frying pan over medium-high heat. When you can feel the heat while holding your hand just above the griddle or pan, cook the patties for 3-5 minutes on each side or until they cooked through. Serve on lettuce or on a bun, with the toppings and condiments of your choice.