• Preheat your oven to 325℉.
• Rub the ends of the roast with the olive oil, then firmly massage the garlic, salt and pepper into the top (the fat cap) of the roast. Nestle it in a large roasting pan, at least 2 inches deep, and place in the center of the oven. Roast for 2-3 hours, basting with the accumulated fat every half hour. At one hour in, add the chopped vegetables to the pan with the thyme, and stir to combine with the drippings.
• At about 2 hours, check the internal temperature by sticking an instant read thermometer into the center of the thickest part of the roast. (Once a roast reaches 100℉ the temperature will rise at an accelerated rate, so check every 10 minutes or so. Try to use the same hole each time, as poking it in many places allows more juices to escape.)
• When the internal temperature has reached 120℉, remove from the oven. Move the roast to a carving block, and cover with foil or an inverted pot, and allow to rest for about 30 minutes. This allows the meat to relax, the juices to redistribute, and makes for an even medium rare as the residual heat raises the internal temperature to 125-130℉.
• Strain off and reserve about 2 tablespoons of fat from the pan (for the Yorkshire Pudding), and increase oven temperature to 425℉. Meanwhile, place the roasting pan with the vegetables over medium heat on the stove, and add the beef stock. Bring to a simmer for 10 minutes, then strain, reserving the jus. Taste for salt, adjust seasoning, and serve.

Yorkshire Pudding

• An hour in advance: Whisk eggs with the salt until frothy. Mix in the flour, whisking constantly. Add the milk in a thin stream, and beat until the mixture is smooth. Chill for an hour.
• Preheat the oven to 425℉.
• In a 12×9 casserole, heat the beef fat (or lard) on the stovetop until it sizzles. Beat the batter once more, adding the cold water. Pour into the sizzling fat, and bake on the top shelf of the oven for 15 minutes. Rotate the dish, lower the heat to 400℉, and cook an additional 15 minutes. It should be well risen, crisp, and brown. Serve very hot with Prime Rib of Beef Au Jus.