In a small bowl, combine the paprika, onion powder, garlic powder, and 1/4 tsp. black pepper. Rub this mixture over the roast. Cover and chill at least 2 hours.
In a 4-qt. Dutch oven, brown the roast on all sides in hot oil over medium heat. Remove the roast. Add onion and garlic to the pot; cook and stir for 30 seconds or until fragrant but not browned.
Add 2 cups chicken broth, 1 cup milk and the orange juice to the Dutch oven, scraping any browned bits from the bottom. Add 1/2 tsp. black pepper, the thyme and cumin. Bring to boiling and return the roast to the Dutch oven.
Cover with foil AND a tightly fitting lid. Roast in a preheated 325-degree oven for 1-3/4 to 2-1/4 hours, until meat is fork tender. Add chicken broth as needed so that meat is half submerged.
Transfer meat to a shallow dish and keep warm. Skim fat from cooking juices. On the stove top, bring the juices to a boil, then reduce heat and simmer, uncovered, for 15 to 20 minutes, or until reduced by nearly half.
In a large saucepan, cook the garlic in butter over low heat for 2 minutes; add 3-1/2 cups chicken broth, 1-1/3 cups milk, 1/4 tsp. pepper and the rosemary. Bring to a low simmer. Add grits in a steady stream, stirring constantly. Cook and stir for 6 to 8 minutes until thickened. Add the cheese and snipped sage.
To serve: shred pork with two forks; moisten with some of the pan sauce. Serve pork over grits, topped with sage leaves.