Mix the turkey, bread crumbs, onion, eggs, apple sauce, chilli powder, paprika and sea salt in a large bowl until thoroughly combined. Divide mixture into 8 equal portions, then shape into patties.
Heat olive oil in a large frying pan over medium-high heat. Arrange the patties in the frying pan then cook until browned, 3 to 5 minutes on each side. Place the browned patties on a paper towel-lined plate to drain. Transfer the patties to an oblong baking dish.
Bake the turkey burgers in the preheated oven until no longer pink in the centre and the juices run clear, about 10 minutes more. Serve the turkey burgers on the hamburger buns.