Step 1 Heat the oven to 375 degrees. Wrap each of the bone ends with foil.
Step 2 Make 2 deep slits between each of the bones on the loin. Top each apricot with a sage leaf and a sliver of garlic and fold in half. Tuck each folded apricot half into a slit in the roast. Season the meat with salt and pepper.
Step 3Heat the butter in a skillet until melted. Add the minced garlic and cook until fragrant, about 1 minute. Stir in the bread crumbs. Add salt and pepper to taste. Place the roast in a roasting pan and top with the crumbs, patting them in place.
Step 4Roast until a meat thermometer inserted in the center of the meat registers 150 degrees, 60 to 75 minutes. Remove to a carving board and let stand while preparing the sauce.
Step 5Combine the one-fourth cup of water and the chicken broth and stir into the drippings in the roasting pan, stirring to loosen any brown bits. Pour into a small saucepan and stir in the port. Bring to a boil, reduce the heat and simmer 5 minutes. Strain, then pour the liquid back into the saucepan. Blend the cornstarch and remaining 1 teaspoon of water until smooth; stir into the saucepan and simmer until the sauce is thickened and clear, 3 to 5 minutes. Season to taste with salt and pepper.
Step 6Remove the foil from the bones. Carve the roast, cutting between the bones. Serve 1 chop with bone per serving, spooning a little sauce over each. Serve 2 roasted chestnuts on each plate.