In large skillet, heat 1 1/2 teaspoons of the oil over high heat. Add carrots, celery, onion and garlic; cook, stirring, about 5 minutes or until vegetables are browned. Remove from skillet. Add the remaining 1 1/2 teaspoons oil and the pork ribs; cook about 5 minutes or until browned.
Transfer pork ribs to 5-quart slow cooker. Top with vegetables. In small bowl, stir together broth and tomato paste; add to cooker. Stir in tomatoes and half of the Italian seasoning and pepper. Cook for 7 hours on low-heat setting or for 5 1/2 hours on high-heat setting.
Skim off fat. Remove pork ribs with a slotted spoon to platter; let cool. Stir remaining Italian seasoning, remaining pepper and the salt into cooking liquid in cooker. Shred pork (or pull into bite-size chunks) and add to cooking liquid. Serve over pasta.