In a large mixing bowl, combine the ground turkey, chopped spinach, crumbled feta, minced red onion, garlic, oregano, salt, and pepper.
Mix the ingredients by hand until just incorporated, ensuring the feta and spinach are evenly distributed without overworking the meat.
Divide the mixture into 4 equal portions and form into patties approximately 1/2 inch thick.
Heat the olive oil in a large non-stick skillet or grill pan over medium-high heat.
Add the patties to the pan and cook for 5 to 6 minutes per side.
Verify that the internal temperature has reached 165 degrees Fahrenheit (74 degrees Celsius) using a meat thermometer.
Remove from the heat and allow the burgers to rest for 2 to 3 minutes before serving.