Heat oven to 400 degrees fahrenheit and remove chops from refrigerator ½ hour before cooking.
Heat a medium cast iron skillet over medium-high heat and add olive oil. Season lamb loin chops with salt and pepper and brown in skillet about 4-5 minutes per side, until a nice crust is formed. Brown fat cap side until deep golden and fat is rendered off of it, about 2-3 minutes.
Pour off all of the excess fat, lay loin chops on their sides and place in the oven. Cook for about 4-5 minutes for 125 degrees or until desired temperature is reached. (Note: meat will continue to cook while resting so you should remove from the oven about 10 degrees less than desired final temperature).
Remove chops from skillet and rest on a plate. Heat skillet over medium, being careful not to burn your hands on the hot handle. Add the garlic, shallots and thyme and toss until caramelized and fragrant, about 2-3 minutes. Spoon over chops and serve.
Recipe by Jackie Ourman at http://jackieourman.com/lamb-loin-chops-with-garlic-shallot-and-thyme/