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1
Let the meat stand at room temperature for 1 hour.
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2
In a small bowl combine the black peppercorns, green peppercorns, white peppercorns, allspice, thyme, and coarse salt. Rub the meat with the mixture.
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3
Roast the meat, rib side down in a roasting pan, in a preheated 500 degrees Fahrenheit oven for 30 minutes, reduce the heat to 350 degrees Fahrenheit.
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4
Roast the meat for 1 hour and 45 minutes to 2 hours more, or until a meat thermometer inserted in the fleshy part of the meat registers 130 degrees Fahrenheit for medium-rare.
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5
Twenty minutes before the roast is done, add the blanched baby carrots, garlic, and shallots, all patted dry, to the pan.
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6
(Remove the vegetables with a slotted spoon if they brown too quickly.).
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7
Transfer the roast to a heated platter, drain the vegetables on paper towels, and keep them warm, covered loosely.
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8
Let the roast rest for at least 20 minutes and up to 30 minutes before carving it.
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9
Make the sauce:
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10
Skim the fat from the pan juices, add the red wine, and deglaze the pan over moderately high heat, scraping up the brown bits.
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11
Boil the liquid until it is reduced by half and transfer it to a saucepan.
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12
Add the beef broth and 1/4 cup of the Madeira wine and boil the mixture for 5 minutes.
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13
In a small bowl stir together the remaining 2 tablespoons Madeira, arrowroot, and the mustard; add the mixture to the pan in a stream, whisking constantly.
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14
Bring the sauce to a boil, whisking, and boil it for 1 minute.
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15
Season the sauce with salt and pepper and transfer it to a heated sauceboat.
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16
Arrange the roasted vegetables around the roast with the fresh thyme and serve the roast with sauce.