In a large bowl, use your hands to combine the turkey, feta, onion, mayo, salt, oregano and pepper to taste. Add in the spinach and breadcrumb, mix again until combined.
Shape into 6 patties. Arrange them on a lightly greased baking sheet and cover loosely with plastic wrap. Refrigerate for at least 30 minutes or for up to a few hours.
Brush or spray them lightly on both sides with olive oil. Prepare a grill for medium-high heat with space to cook over direct heat. Once it's ready, add the burgers. Cook them for 4-6 minutes on each side, until grill marks appear and the burgers are cooked through. You can also pan sear these if you don't have a backyard BBQ.Serve with your favorite toppings and condiments.