Combine first 9 ingredients in a large mixing bowl; toss to combine.
Fill a large shallow pan with warm water. Gently soak 1 rice paper wrapper in water until malleable; place on a flat work surface. Place 1/2 cup of veggie filling toward one side of wrapper; top with 1 avocado slice. Fold in ends of wrapper; roll tightly to enclose. Repeat with remaining wrappers and filling. Serve with Cashew-Ginger Dipping Sauce.