Preheat the oven to 350°F.

In a bowl, add the turkey, egg, feta, cream cheese, tomato, white onion, garlic, cumin, oregano, sea salt, and black pepper. Stir to combine well. Form the turkey into 4 patties, about 1⁄2 inch thick.

In an ovenproof skillet, heat the oil over medium heat. Add the burgers and cook them for about 4 minutes on each side. Transfer the skillet to the oven and cook for 7 to 8 minutes, or until the burgers are completely cooked through and a meat thermometer inserted in the thickest part of the burger registers 165°F. Remove the burgers from the pan and serve immediately. Serve on lettuce leaves with desired toppings.