Pour the teaspoon of olive oil in a heavy skillet with a tight fitting lid over high heat. When it is shimmery and hot add the roasted garlic to the pan and stir for about 10 seconds or until it's fragrant. Add the spinach all at once and flip it a couple of times with tongs. Turn the heat off, add the lid and let sit for 2 minutes. Remove the lid, flip a couple more times, add the lid and leave for 1 more minute. Use the tongs to gently transfer the spinach and garlic to a colander on a plate. Let it rest until room-temperature. Either chill in a tightly covered container in the refrigerator for up to 3 days or proceed to the next step.

Roughly chop the wilted spinach and garlic so you can more easily mix it through the ground turkey. Add it to a mixing bowl with the turkey, feta, salt, and pepper. Gently but thoroughly mix everything together until all of the ingredients are evenly distributed. Form into 4 to 6 burger patties that are at least 3/4 of an inch thick. Place the formed patties onto a parchment lined cookie sheet and let it rest in the freezer while you preheat your grill.

Preheat your grill to medium-high. Soak a wadded paper towel generously with olive oil and use tongs to rub it over the clean grill grates, heavily oiling them. Ease the burger patties onto the grill and do not move them for 6 minutes, leaving the cover of the grill open. After 6 minutes, flip the burgers just once and let them continue to cook for 8-10 minutes, or until the burgers release from the grill and the interior temperature of the thickest part of the burgers reaches 165°F. Transfer the burgers to a clean plate.

Brush each of the insides of the buns with olive oil and toast them directly on the grill just until they have grill marks. Use tongs or a spatula to transfer the buns to a clean plate or baking sheet.

Serve each burger on a bun topped as desired.