Make the burgers: Combine the turkey, feta, spinach, kalamata olives, shallot, ½ teaspoon garlic, 2 teaspoons oregano, salt (go lightly on the salt—the feta and olives are saltand pepper to taste in a bowl, using your hands unless you just feel like you need to use a spoon.
Divide the mixture into 4 equal portions, and form a patty with each. Use your fingers to form a small indent in the middle of each patty. This will allow the patties to end up flat after they have been cooked.
Preheat the grill to medium high, or preheat a nonstick or cast iron pan. Grill or pan sear the burgers for about 5 minutes on each side, or until cooked through.
Serve the burgers hot on the buns with tzatziki, lettuce, tomatoes and onions, as desired.