Place pork roast in 4- to 6-quart slow cooker. In small bowl, combine gingerroot, sherry, garlic and 3 tablespoons of the hoisin sauce; mix well. Spoon mixture over roast. Snap off and discard stems from dried mushrooms; crumble mushrooms over roast.
Cover; cook on low setting for 8 to 10 hours.
About 15 minutes before serving, heat oven to 300°F. Brush tortillas with sesame oil; stack on sheet of foil. Wrap tightly. Heat packet at 300°F. for 10 minutes.
Meanwhile, remove pork from slow cooker; place on large plate. Stir cabbage into juices in slow cooker. Increase heat setting to high; cover and cook an additional 5 minutes or until cabbage is wilted.
Shred pork with 2 forks; return to slow cooker. Spread each warm tortilla with 1 teaspoon remaining hoisin sauce. Top each with about 3/4 cup pork mixture and 1 tablespoon onions; roll up.