Roasted Rack of Lamb with Red Wine Pan Sauce and Rosemary

FOR THE LAMB:
Adjust oven rack to lower-middle position, place shallow roasting pan or jelly-roll pan on oven rack, and heat oven to 425 degrees.

Season lamb with salt and pepper. Heat oil in heavy-bottomed 12-inch skillet over high heat until shimmering. Place racks of lamb in skillet, meat-side down in the center of the pan, with ribs facing outwards; cook until well-browned and nice crust has formed on surface, about
4 minutes. Using tongs, stand racks up in skillet, leaning them against each other to brown the bottoms; cook until bottom sides have browned, about 2 minutes longer.

Transfer lamb to preheated roasting pan. (Begin pan sauce.) Roast until instant-read thermometer inserted into the center of each rack registers about 135 degrees, 12 to 15 minutes, depending on size of rack. Cover meat loosely with foil and let rest about 10 minutes. Carve, slicing between each rib into individual chops, and serve immediately with the sauce.

FOR THE SAUCE:
Pour off all but 1 1/2 tablespoons fat from skillet used to brown lamb; place skillet over medium heat. Sauté shallots until softened, about 1 minute. Add red wine and rosemary; increase heat to medium-high and simmer until dark and syrupy, about 7 minutes. Add chicken broth; simmer until reduced to about 3/4 cup, about
5 minutes longer. Off heat, swirl in butter; season to taste with salt and pepper, and serve with lamb.