Heat the oven to 450°F. Mix 2 tablespoons olive oil with the garlic, rosemary, thyme, 1 teaspoon salt, and 1/2 teaspoon pepper. Rub this mixture all over the prime rib roast and place it in a roasting pan.
Roast the beef for 20 minutes, then lower the temperature to 325°F. Continue cooking until the internal temperature reaches 130°F for medium-rare, about 1 hour and 15 minutes. Remove the roast to rest and pour the drippings into a measuring cup.
While the beef roasts, toss the carrots, parsnips, potatoes, and onion with the remaining 1 tablespoon olive oil, 1/2 teaspoon salt, and 1/2 teaspoon pepper on a baking sheet. Add the sheet to the oven during the last 45 minutes of beef cooking.
Raise the oven temperature to 425°F. Whisk the flour, eggs, milk, and remaining salt until smooth. Spoon 1 teaspoon of reserved drippings into each cup of a 12-cup muffin tin and heat the tin for 5 minutes. Fill each cup halfway with batter and bake for 20 minutes until puffed and golden.
Slice the rested roast and serve with the Yorkshire puddings and roasted vegetables.