Not only is pork shoulder roast more budget-friendly than pork chops or a pork loin, but it also has rich flavor and is very versatile. Braising, roasting, or stewing all result in moist, tender meat.
Preheat oven to 350 degrees. Season pork with salt and pepper. In a large Dutch oven or other heavy pot, heat 1 tablespoon oil over medium-high. Add pork, fat side down, and cook, turning until browned on all sides, 8 minutes. Transfer pork to a plate. Pour off fat, return pot to medium-high, and add remaining tablespoon oil. Add onion; cook until translucent, 5 minutes. Add garlic; cook until fragrant, 30 seconds. Add tomatoes; season with salt and pepper. Add broth and vinegar and cook, stirring and scraping up browned bits. Return pork to pot with juices; sprinkle with paprika.
Bring mixture to a boil over high. Cover, transfer to oven, and cook 1 hour. Remove from oven; with tongs, flip pork. Return to oven and cook, uncovered, until tender, 1 hour, basting pork with juices every 15 minutes. Transfer pork to a cutting board; let rest 15 minutes. Slice pork and serve with sauce.