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For beef:.
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Sprinkle entire surface of beef tenderloin with coarse kosher salt.
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Place beef on rack set over large rimmed baking sheet.
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Refrigerate uncovered at least 24 hours and up to 36 hours.
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For sauce:.
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Melt 2 tablespoons butter in large saucepan over medium-low heat.
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Add shallots; saute until soft, 3 minutes.
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Add Cognac, rosemary, and 1 teaspoon cracked pepper and cook until liquid evaporates, 1 minute.
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Add Port; bring to simmer.
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Add all of beef stock.
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Boil until reduced to 1 1/2 cups, about 20 minutes.
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Strain into medium saucepan, pressing on solids to extract as much liquid as possible.
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Discard solids in strainer.
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DO AHEAD: Can be made 24 to 36 hours ahead.
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Cool slightly, then cover and chill.
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For roasting:.
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Let beef stand at room temperature 1 hour before roasting.
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Position rack in center of oven and preheat to 425F Rub beef all over with oil; sprinkle with 2 tablespoons cracked peppercorns, pressing to adhere.
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Return beef to rack on baking sheet and roast until instant-read thermometer inserted into thickest part of meat registers 125F for medium-rare (135F to 140F in thinnest part), about 30 minutes.
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Remove roast from oven and let rest 15 minutes.
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Bring sauce to boil; whisk in remaining 2 tablespoons butter.
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Season sauce to taste with salt and pepper.
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Cut off string from roast.
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Cut roast crosswise into 1/2-inch-thick slices; arrange on platter.
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Serve with sauce.