Heat grill. In medium bowl, combine teriyaki baste and glaze and gingerroot; mix well. Add chicken; stir to coat.
When ready to grill, place chicken in grill basket. Place basket on gas grill over medium-high heat or on charcoal grill 4 to 6 inches from medium-high coals. Cook 10 to 12 minutes or until chicken is no longer pink in center, stirring frequently.
In small bowl, combine coleslaw and mint; mix well. Cut large chicken strips into smaller pieces. In center of each lettuce leaf, spoon a few chicken strips. Top each with about 2 tablespoons coleslaw mixture. Fold up bottom of each lettuce leaf; roll to enclose filling.