In a large mixing bowl, combine the ground turkey, crumbled feta, chopped spinach, minced red onion, minced garlic, oregano, salt, and pepper.
Mix the ingredients by hand until just combined, ensuring the feta and spinach are evenly distributed without overworking the meat.
Divide the mixture into four equal portions and shape into patties approximately 3/4 inch thick.
Preheat a cast-iron skillet or grill over medium-high heat and add the olive oil to coat the surface.
Cook the patties for 5 to 6 minutes per side until well-browned and the internal temperature reaches 165°F (74°C).
Remove the patties from the heat and allow them to rest for 3 minutes before serving to retain juices.