Pour beef broth into slow cooker and add pork ribs. Cook on High until meat shreds easily, about 4 hours. Remove meat and shred with two forks.
Preheat oven to 350 degrees F (175 degrees C). Transfer shredded pork to a Dutch oven or skillet and stir in carrots, barbecue sauce, and mesquite sauce.
Bake in preheated oven until heated through, about 30 minutes.