30 minutes before cook time, remove the lamb chops from the fridge. Drizzle with olive oil and evenly distribute salt over all sides of the lamb. Use salt according to taste.
Place 1 tablespoon olive oil, half of the shallot and 2 garlic cloves into a cast iron skillet. Warm the pan over high heat. Once the pan is hot, add 1 tablespoon unsalted butter to the pan. Let it quickly melt.
Quickly place half of the lamb chops into the skillet. Cook 3-4 minutes per side, for rare (for medium cook longer), for a total of 6-8 minutes.
Remove the lamb and place onto a platter. Cover.
Wipe out the cast iron using tongs and a paper towel. Discard the shallot and garlic.
Repeat steps 2-4 with the last batch of lamb chops.
Serve with feta yogurt sauce.