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1
Season the steaks generously on all sides with salt and let them sit at room temperature for 45 minutes to an hour.
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2
Heat the oven to 350 degrees Fu00b0 and place a wire rack inside a rimmed baking sheet.
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3
Set a heavy pan large enough to hold all four steaks over medium-high heat. Once the pan is hot, add the oil. When it starts to smoke, lay the steaks in the pan and don't touch them for 2 minutes. Peek underneath one of the steaks, and if it's nice and brown, flip the steaks over; if it's not, leave the steaks for another minute or so and check again. Cook the steaks on the second side for another 2 minutes, then transfer them to the wire rack.
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4
Put the steaks in the oven. Start checking the temperature after about 8 minutes (for medium rare, a thermometer inserted into the thickest part of the steak should read 130 degrees Fu00b0). When they're cooked to your liking, transfer the steaks to a cutting board and let them rest for at least 5 minutes.
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5
While the steaks are in the oven, make the sauce. Set the pan you used to cook the steaks over medium heat and add the shallots and the crushed black peppercorns. Cook, stirring every once in a while, until the shallots soften and gently caramelize. Pour in the Cognac and cook until the liquid has mostly evaporated. Add the stock, turn up the heat and boil until the sauce becomes thick and slightly syrupy (it should reduce by about 80%). Add the cream and bring to a boil, then quickly remove the sauce from the heat. Strain it through a fine mesh sieve into a small pot to remove the crushed peppercorns, then stir in the green peppercorns, cover the pot and keep the sauce warm until you're ready to eat.
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6
To serve, spoon a generous amount of sauce over the top of each steak.
