Coat all sides of roast with olive oil.
In a small bowl, combine paprika, rosemary, garlic powder, salt, and pepper. Rub over entire roast.
Heat a little olive oil in a skillet over medium-high heat. Add meat, and sear on all sides until evenly browned.
Place roast, onion, celery, and carrots in a slow cooker. Add enough water to cover the bottom by ¼ inch.
Cover and cook on low for 7 to 8 hours, or until meat pulls apart easily.
Remove meat and set aside to rest for 20 to 30 minutes before shredding.
Enjoy as a sandwich, wrapped in a tortilla, or as a stand-alone pulled pork dish with sauce.
