Remove the lamb chops from the refrigerator. Massage the chopped thyme, 1/2 teaspoon kosher salt, and black pepper into both sides of the meat. Let the chops sit at room temperature for 5 minutes.

Melt 2 tablespoons of butter in a 12-inch skillet over medium-high heat. Once the butter is hot, add the lamb chops in a single layer.

Cook the lamb without moving it until a deep brown crust forms on the bottom, about 4 to 6 minutes. Thicker chops may need closer to 10 minutes on the first side.

Flip the lamb chops and continue cooking until an instant-read thermometer inserted into the thickest part registers 145°F, about 4 to 6 minutes more.

Transfer the lamb chops to a plate and cover loosely with aluminum foil. Pour off all but 2 tablespoons of the rendered fat from the skillet.

Reduce the heat to medium. Add the shallot, smashed garlic, and thyme sprig to the pan. Cook for about 1 minute, until the shallot softens and starts to brown.

Add the wine or broth and lemon juice, scraping the browned bits from the bottom of the pan. Cook until the liquid reduces by half, about 1 to 2 minutes.

Stir in the lemon zest, remaining 1/4 teaspoon salt, and remaining 2 tablespoons butter. Cook until the butter melts and the sauce thickens slightly. Taste, adjust with more salt and pepper if needed, then pour the sauce over the lamb chops and serve immediately.