In a large mixing bowl, combine the ground turkey, cheddar cheese, chopped jalapeño, breadcrumbs, cilantro, garlic powder, onion powder, smoked paprika, salt, and black pepper. Mix until just combined; do not overmix.
Divide the mixture into four equal portions and shape each portion into a patty about 3/4 inch thick.
Heat the olive oil in a large skillet over medium heat. Once hot, add the patties to the skillet. Cook for about 5-6 minutes on each side, or until the internal temperature reaches 165°F.
While the burgers are cooking, toast the burger buns in a separate skillet or under the broiler until golden brown.
Assemble the burgers by placing a patty on each bun and topping with lettuce, tomato, and avocado as desired. Serve immediately.