In a large mixing bowl, combine the ground turkey, panko breadcrumbs, egg, Worcestershire sauce, ketchup, Dijon mustard, dried parsley, garlic powder, onion powder, 1 tablespoon olive oil, and generous pinches of salt and pepper. Use your hands or a fork to mix everything together until just combined — do not overwork the meat.

Divide the mixture into 4 equal portions and shape each into a patty about 3/4-inch thick. Make a slight indentation in the center of each patty with your thumb to help them cook evenly.

Place a cast-iron grill pan or a heavy skillet over medium heat and brush lightly with olive oil. Once hot, add the patties in a single layer (cook in batches if needed). Cook for 3 to 4 minutes per side, until the internal temperature reaches 165°F when checked with an instant-read thermometer. Do not press down on the patties while cooking.

Lightly toast the burger buns if desired. Spread a thin layer of mayo on the bottom bun, then add a lettuce leaf, the cooked turkey patty, a generous spoonful of mashed avocado, a drizzle of salsa (if using), and slices of tomato and red onion. Finish with the top bun and serve immediately.