In a large skillet, heat the olive oil over medium heat. Add the sliced red onions and a pinch of salt. Cook for about 15-20 minutes until soft and golden brown.
In a mixing bowl, combine the ground turkey, egg, parsley, curry powder, garlic powder, Worcestershire sauce, salt, and black pepper. Mix gently until combined.
Divide the turkey mixture into four portions and shape into patties, slightly larger than the buns.
In the same skillet, add the patties and cook for 5-6 minutes on one side until golden brown. Flip and cook for another 5-6 minutes until the internal temperature reaches 165°F (74°C).
Assemble the burgers by placing patties on buns, topping with caramelized onions and any additional toppings.