Braising is typically used for simmering tough meats for hours, but it works beautifully (and much more quickly!) with tender cuts, too. We paired lamb chops with rosemary and garlic for big flavor, fast.
Season lamb with salt and pepper. Heat a large straight-sided skillet over medium-high. Add oil, then lamb in a single layer. Cook, flipping once, until browned on both sides, 5 to 7 minutes. Transfer to a plate.
Reduce heat to medium. Add onions; cook, stirring a few times, until golden brown in places, 5 to 7 minutes. Add garlic, rosemary, and tomato paste; cook until fragrant, about 1 minute. Add wine; cook until mostly evaporated, about 1 minute. Stir in broth. Return lamb and any juices to pan; bring to a simmer. Partially cover, reduce heat to low, and cook until a thermometer inserted in thickest part of lamb (without touching bone) registers 130 degrees, 6 to 8 minutes. Serve over potatoes.