Preheat oven to 350ºF and set the oven rack to the middle position. Also, on the stovetop, preheat a large cast iron skillet over medium high heat.

Drizzle olive oil over the meat and rub to coat evenly. Generously cover with kosher salt and freshly ground black pepper.

Using tongs, sear the meat on all sides until you have a nice brown crust. (2-3 minutes on each side). When browned, stand racks of lamb up and lean them against each other while interlocking the bones.

Place the skillet in the oven and roast for 15 minutes. Next tent the lamb with aluminum foil, covering just the bones. Cook for another 10-25 minutes, until the internal temperature of the meat reaches 135ºF.

Remove the meat from the skillet to a plate and cover with foil. Put the skillet on the stove over medium heat and add the chopped shallots to the pan. Sauté until beginning to brown (about 5 minutes).

Add 1/2 cup of cognac to the pan and scrape up the brown bits. Simmer for 2 minutes. Add the heavy cream and dijon mustard and gently simmer until sauce is thick enough to coat the back of a spoon (about 5 minutes). Add the parmesan and stir until well combined. Lastly, add the rosemary, remaining cognac, and salt and pepper to taste.

Cut the meat into individual chops and serve in a pool of the sauce and with more sauce on the side.