Add ground turkey, cooked quinoa, oats, egg, oregano, garlic powder, parsley, salt, cayenne pepper, red onion, and feta cheese to a large bowl. Stir together until completely combined, but try not to overmix.
Shape into 6 patties, and cook until burgers are cooked through.
To cook, heat a large skillet over medium-high. Add oil and swirl around skillet. Place burgers in one layer and cook for about 4-5 minutes per side. If you skillet is smaller, you can do this in batches [use 1 tablespoon of oil per batch].
Serve each burger on a hamburger bun with a tomato slice and a few cucumber slices. Enjoy!