Preheat the oven to 375°F. Line a large roasting pan with foil and oil the foil. Place roast on foil.
In a small bowl, combine garlic, oil, rosemary, pepper and 2 teaspoons salt. Rub mixture all over pork meat (but not on bones), inside and out. If you like, place a small ovenproof ramekin or a bowl in the center of roast to help it keep its shape. Wrap tips of bones with small pieces of foil to prevent them from burning. Roast pork in center of the oven until just browned on the outside, about 1 hour.
Meanwhile, in a medium saucepan, combine broth, onion, celery, butter and remaining 3/4 teaspoon salt, and bring to a boil. Stir in rice. Lower heat, cover the pan and simmer until rice is tender, 40 to 50 minutes. Add cranberries, pecans and 2 teaspoons thyme leaves, and toss. Remove from heat.
Remove pork from oven; remove ramekin. Toss rice and mound in center of pork; if some doesn’t fit, transfer to a small baking dish and roast alongside the pork. Continue to roast until an instant-read thermometer inserted into the center of chops (but not touching bone) registers 150°F, 20 to 30 minutes more. Let rest 15 minutes.
Using 2 spatulas, carefully transfer roast to a platter; replace any stuffing that falls out. Remove and discard foil tips and any string used to tie roast. Sprinkle top of rice with remaining 1 teaspoon thyme. Carve between bones and serve each chop with rice stuffing.