Make the spice rub: Add the mulling spice to a small dry skillet over medium heat. Cook, tossing constantly, until toasted and fragrant, about 2 minutes. Transfer to a mortar and pestle or spice grinder and grind to a fine powder (a few larger chunks are okay). Mix in the salt and a few grinds of black pepper.
Drizzle the lamb with about 1 tablespoon of olive oil (a very light coating) and rub all over with your ground mulling spice. If you’re not in a rush, set the lamb on a wire rack set in a rimmed baking sheet and refrigerate, uncovered until ready to cook (this will help intensify the flavor of the rub). If not, no worries, your lamb will still be deliciously flavorful.
Add 1 tablespoon of butter to a large cast-iron skillet and heat over high heat. Once shimming, add in the lamb, meaty side down. Cook until lightly-charred, about 2-3 minutes. Using tongs, flip the lamb and continue cooking until lightly browned on the other side, about 2 minutes more.
Using your tongs, stand the racks so the bones are pointing up and sear the underside of the lamb for about 1 minute.
Add the remaining butter to the pan and reduce the heat to medium-low.
Cove and cook, flipping and basting occasionally, until an instant-read thermometer registers 130 degrees for medium-rare, or 135 degrees for medium, about 15-20 minutes.
Drizzle with more brown butter sauce and top with fresh parsley. Let rest at least 5 minutes before slicing alongside rice pilaf or your favorite vegetable or grain.
