Make the spice rub: In a small bowl, mix fresh herbs, minced garlic, melted ghee, salt, and pepper to form a paste. Pat lamb chops dry and rub the mixture evenly over both sides. Let sit 10–15 minutes at room temperature (or refrigerate for up to 4 hours, then bring to room temp before cooking).
Sear the chops: Heat 2 tablespoons ghee in a large skillet or Dutch oven over medium-high heat. Sear lamb chops for 3–4 minutes per side, until deeply browned. Transfer to a plate.
Sauté the vegetables: In the same pan, add onion, bell peppers, and mushrooms. Sauté 4–5 minutes, scraping up any browned bits with a wooden spoon.
Deglaze and build the sauce: Whisk arrowroot starch into the broth to make a slurry. Pour into the pan, stirring well to deglaze and slightly thicken the mixture.
Braise: Return the lamb chops (and any juices) to the pan. Reduce heat to low, cover, and cook for 20–25 minutes, or until lamb is tender and easily pierced with a fork. Stir occasionally to ensure the vegetables don’t stick.
Finish & serve: Remove from heat and let rest, covered, for 5 minutes. Taste and adjust seasoning. Garnish with fresh herbs and a squeeze of lemon juice, if desired.