If you are grilling the burgers, grease the grates of your grill and preheat it to between medium-high heat (about 375°F ). If baking the burgers in the oven, preheat your oven to 350°F, line a rimmed baking sheet with aluminum foil and grease the foil with cooking oil. Set the baking sheet aside.
In a large bowl, place the egg yolks, parsley, garlic, onion, chile, paprika, cumin and salt, and mix to combine well. Add the feta cheese, and mix gently to combine. Add the turkey, and mix gently until the other ingredients are evenly distributed throughout the ground meat. With wet hands, divide the meat mixture into 8 portions and form into patties that are about 1/2 inch larger than the bun on which you are serving them.
If grilling the burgers, cook them for about 7 to 8 minutes per side. If baking the burgers, place the burgers on the prepared baking sheet about 1 inch apart from one another and bake for about 30 minutes or until the juices run clear. Remove the burgers from the grill (or the oven), cover with foil and allow to rest 10 minutes before placing each burger on a bun and serving.