How to Make It
Coat the steak with 2 tablespoons each of salt and pepper. Press 1 thyme sprig onto each side of the steak and let stand at room temperature for 1 hour.
Preheat the oven to 350°. In a small saucepan, melt the butter. Add the minced shallot and garlic and cook over low heat until softened. Add the green peppercorns, the remaining thyme sprig, the mustard and 1 teaspoon of pepper and cook for 1 minute, stirring. Add the Armagnac and cook over moderate heat until reduced by half, about 5 minutes. Add the red wine and simmer until reduced by half, about 15 minutes. Stir in the demiglace and simmer until slightly reduced, about 5 minutes. Add the cream and simmer until the sauce is reduced to 1 1/2 cups, about 10 minutes. Discard the thyme sprig.
Heat the oil in a large cast-iron skillet. Add the steak and cook over moderately high heat, turning once, until crusty and browned, 7 minutes total. Transfer the steak to the oven and roast, turning once, until cooked to 125°, 18 to 20 minutes. Transfer the steak to a cutting board and let stand for 10 minutes, then carve the meat from the bone and slice it. Serve with the green peppercorn sauce and The Cheesiest Mashed Potatoes.
The peppercorn sauce can be refrigerated overnight.