1 (4-rib) standing beef rib roast (bone-in prime rib; 9 to 10 pounds)
1/4 cup mixed peppercorns (pink, white, and green)
3 tablespoons plus 2 1/2 teaspoons kosher salt, divided
2 tablespoons chopped fresh thyme
2 tablespoons chopped fresh rosemary
1 tablespoon extra-virgin olive oil
3 pounds medium Yukon Gold potatoes, peeled and each cut into 6 wedges (keep in a bowl of cold water to prevent discoloration)
3 pounds carrots, peeled and cut diagonally into 2-inch pieces
1 (750 milliliter) bottle Pinot Noir
1/2 cup chopped shallots
4 tablespoons unsalted butter, divided
2 1/4 cups reduced-salt beef or chicken broth