Adjust oven rack to upper-middle position and heat oven to 250ºF.
Heat oil in a small skillet over medium-low heat. Add 12 whole garlic cloves and cook, stirring occasionally, until soft and golden, about 5 minutes. Remove with a slotted spoon; reserve oil.
Turn pork loin fat-side down. Slit lengthwise, almost but not quite the whole way through, to form a long pocket, leaving a ½-inch border of unslit meat at each end. Brush cavity with some of the reserved garlic cooking oil, and sprinkle generously with salt and pepper and 1 tablespoon of the rosemary. Line cavity with sautéed garlic and apricots; sprinkle with cranberries. Tie loin together with cooking twine at 1 ½-inch intervals.
Brush meat with remaining oil, and sprinkle generously with salt and pepper. Set roast, fat-side up, diagonally across a large sheet pan.
Warm ¼ cup apple jelly along with the pressed garlic and rosemary. Brush mixture onto meat.
Roast until a meat thermometer stuck into the center registers 125 to 130 degrees. (Start checking at about 1 ½ hours.)
Remove from oven; raise oven temperature to 400 degrees. Brush loin with pan drippings, return to oven, and continue to roast until the loin is golden brown and a meat thermometer stuck into the center registers 155 to 160 degrees, about 20 minutes longer. For even more attractive coloring, broil until spotty brown, 3 to 5 minutes.
Let roast rest 15 to 20 minutes; transfer to a carving board. Stir juices around pan to loosen brown bits. Mix chicken broth with cornstarch in a small bowl. Pour drippings through a strainer into a small pan, and stir in alcohol, chicken broth with cornstarch and remaining 2 tablespoons of jelly; whisk into sauce. Simmer until slightly thickened.
Slice pork. Serve each slice with sauce poured on top.