For the Chimichurri
Mince the parsley and garlic. Combine with oregano, salt, chile flake, oil, and vinegar. Stir to combine and reserve.

Chop the olives roughly and mix together with minced preserved lemon, reserve.

In a blender or food processor, combine the Greek yogurt, olive oil, lemon zest, and 2 ounces of the feta cheese. Pulse until smooth and reserve.

Form the lamb into 4 equal sized balls. Flatten the balls and place a tablespoon of whipped feta and a 1 ounce chunk of feta in the center of 2 of the flattened patties. Top each with another flattened patty to create 2 stuffed burgers. Seal the edges to prevent ruptures during cooking. Season the patties on both sides with salt, pepper, oregano, and red chile flakes.

Prepare a charcoal grill to cook over indirect heat. Once the charcoal is hot, add a small chunk of oak to the coals to create smoke. Place your stuffed lamb patties on the grill offset from the fire. Smoke for 20 to 30 minutes at 300 degrees F, until the patties are cooked to desired temperature.

Move the patties to the hot side of the grill to sear briefly before removing them from the heat to rest for 5 minutes.

Toast the buns on both sides. Spread the olive mix on the bottom bun, then top with the patty, then the Chimichurri, and finish with the top bun.