In a mixing bowl, combine the ground turkey, breadcrumbs, grated Parmesan cheese, mayonnaise, minced garlic, onion powder, dried oregano, salt, and black pepper. Mix until all ingredients are well incorporated.
Divide the turkey mixture into 4 equal portions and shape them into patties, about ¾ inch thick.
Preheat the grill or grill pan over medium-high heat.
Once hot, place the turkey patties on the grill. Cook for 5-6 minutes on one side. Flip the patties and cook for an additional 4-5 minutes, or until the internal temperature reaches 165°F (74°C).
During the last minute of cooking, you can toast the burger buns on the grill if desired.
Assemble the burgers by placing the turkey patty on the bottom half of the bun. Top with lettuce, tomato, and onion slices. Add any additional condiments.
Place the top half of the bun over the toppings and serve immediately.