1. To make Pulled Pork, place roast in 3- to 4-quart slow cooker. Combine pear, brown sugar, sriracha sauce, and grated ginger; pour over roast. Cover and cook on Low 8 to 10 hours (High: 4 to 5 hrs.)
2. To make Pickled Vegetables, place carrot, onion and cucumber in non-metal bowl. Combine ginger, rice vinegar, water, sugar, sriracha sauce, salt and minced garlic in small saucepan; cook and stir over medium-high heat until sugar is dissolved. Pour vinegar mixture over vegetables, pressing down vegetables to make sure they are covered. Cover and refrigerate at least 1 hour before serving, occasionally stirring. Remove ginger before serving.
3. Remove roast from slow cooker; strain juices and add pear mixture to the meat. Use tongs or 2 forks to pull pork. Stir in Korean BBQ sauce. Serve over hot rice with pickled vegetables on the side, or make Korean BBQ tacos using flour tortillas.