In a large mixing bowl, combine the panko breadcrumbs and Worcestershire sauce first and let them sit for 2 minutes so the crumbs soften. Add the ground turkey, egg, minced garlic, diced onion, smoked paprika, salt, and pepper, then mix with your hands just until combined, no more than 30 seconds.
Divide the mixture into 4 equal portions, about 4 ounces each, and shape each into a patty roughly 4.5 inches wide and 3/4 inch thick. Press a shallow dimple into the center of each patty with your thumb to stop the middle from puffing up as it cooks.
Heat a cast iron grill pan or skillet over medium heat for 2 to 3 minutes. Add the olive oil and swirl to coat the surface; the pan is ready when a drop of water sizzles and evaporates within a second.
Place the patties in the pan without crowding them and cook for 5 to 6 minutes on the first side without moving them, so a crust forms. Flip once, then cook for another 5 to 6 minutes on the second side, checking the internal temperature at the thickest point and pulling the patties at 165°F.
If using cheese, add a slice to each patty during the last minute of cooking. Cover the pan loosely with a lid or a sheet of foil to trap heat and melt the cheese evenly.
Split the buns and toast the cut sides in the same pan for about 1 minute, until golden. Spread burger sauce or condiments on the bun bottoms, layer lettuce, the patty, tomato, and red onion, then close with the bun top.