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.
Notes
Unless you really, really feel the need to use a spoon, the best way to combine ground meat with other ingredients is with your hands, It helps you combine the ingredients the most thoroughly and prevents crushing the meat and ingredients, which can lead to denser burgers.