Preheat oven to 450 degrees F. For apricot stuffing, in a medium saucepan, combine apricots, 1-3/4 cups chicken stock, and 1/4 cup water. Reduce heat and simmer, covered, for 15 minutes. Uncover and simmer 5 to 10 minutes more or until apricots are soft and broth reduces to a thick syrupy consistency. Cool completely. Stir in the bread crumbs; set aside.
Place the dried mushrooms in a small bowl. Pour 1-1/4 cups of boiling water over the mushrooms; let stand for 5 minutes. Strain mushrooms through a fine mesh strainer, reserving liquid; rinse mushrooms and set both mushrooms and liquid aside. In a very large bowl, combine the onions, carrots, celery, garlic, 2 tablespoons rosemary, 1-1/2 teaspoons kosher salt, and pepper. Stir in 1-3/4 cups chicken stock, mushrooms and mushroom liquid. Set aside.
Set the roast, rib bones down, on a work surface. Don't trim off fat from top of loin meat. Insert the blade of a thin long knife into one end of the roast about 1 inch from top and carefully slice open a pocket about 3 inches wide in the loin. If the roast is very long, insert the blade on the other side of roast to cut pocket so it runs through like a tunnel. Be sure the pockets meet in the center.
Spoon as much of the apricot stuffing as you can into the pocket. Reserve any remaining apricot stuffing. Place the stuffed roast, bone side down, in a shallow roasting pan. Brush roast with olive oil. Sprinkle with 1 tablespoon rosemary and 1 teaspoon kosher salt. Stir any remaining stuffing into vegetable mixture. Spoon vegetable mixture into the roasting pan around the roast. Cover roasting pan with foil.
Roast, in preheated oven, for 45 minutes. Reduce oven temperature to 350 degrees F. Uncover and roast 1-1/4 to 1-1/2 hours more or until an instant-read thermometer inserted near the center registers 155 degrees F.
Remove roast from roasting pan and transfer to a large serving platter. With a slotted spoon remove vegetables from roasting pan. Spoon vegetables around the roast. Cover meat and vegetables with foil; let stand for 15 minutes. (The temperature of the meat after standing should be 160 degrees F)
Meanwhile, strain the cooking liquid through a fine-mesh strainer. Skim off fat. Add enough stock, if necessary, to equal 3 cups. Combine cornstarch and 2 tablespoons cold water in a medium saucepan. Whisk in the cooking liquid. Cook and stir over medium heat until sauce is slightly thickened and bubbly; cook and stir for 2 minutes more.
To serve, slice roast between the rib sections. Spoon some of the warm sauce over the sliced roast. Serve with the roasted vegetables and any remaining sauce. Makes 8 servings.