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1
Season the racks all over with salt and pepper. If you have more than 1 hour and up to 24 hours before you need to serve the lamb, set the racks uncovered on a wire rack set in a rimmed baking sheet and refrigerate until ready to cook. If not, proceed immediately to cooking.
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2
In a large stainless-steel, cast iron, or carbon steel skillet, heat oil over medium-high heat until shimmering. Add racks meaty side down and cook until lightly browned, about 2 minutes. Using tongs, turn racks meaty side up and cook until lightly browned on the underside, about 2 minutes (the ribs curve, so the underside won't make complete contact with the pan). Stand the racks, so the bones are pointing upwards, and sear so that the underside is lightly browned (you may need to lean the racks against each other to keep them from falling).
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3
Add butter, garlic, and thyme to the pan and let melt. Lower heat to medium and cook the lamb, flipping the racks often and basting constantly with the hot butter, until an instant-read thermometer inserted into the eye of the loin registers 130u00b0F (54u00b0C) for medium-rare or 135u00b0F (57u00b0C) for medium, about 20 minutes (though please note that the cooking time will vary heavily depending on the size of the racks, which range from quite small to big and meaty); make sure to spend some time basting the ribs side of the racks so that they cook there too.
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4
Let rest 5 minutes, then carve into individual chops and serve.
