1. Sprinkle pork with pepper. Heat a large skillet over medium-high heat. Add pork; cook 3 minutes on each side or until browned. Transfer pork to a 3-quart slow cooker coated with cooking spray. Add 1 cup water and next 4 ingredients (through garlic) to slow cooker. Cover and cook on LOW for 8 hours or until tender.
2. Remove pork from slow cooker; place in a bowl. Shred pork with 2 forks. Pour cooking liquid through a sieve into a bowl, reserving shallots and garlic. Add 3/4 cup strained cooking liquid, shallots, and garlic to pork; toss well. Discard remaining cooking liquid.
3. Combine mayonnaise and horseradish in a small bowl. Spoon about 2 tablespoons pork mixture on bottom half of each bun. Top evenly with arugula. Spread 1 1/2 teaspoons mayonnaise mixture on cut side of each bun top. Cover sliders with bun tops.