Cut chops into thin strips. Mix barbecue sauce and 1 Tbsp. ginger until blended.
Heat dressing in large skillet on medium-high heat. Add meat, in batches; cook and stir 2 min. or until no longer pink. Remove from skillet; cover to keep warm.
Add onions to skillet; cook and stir 3 min. Stir in cabbage, mushrooms, bean sprouts, peppers and remaining ginger; cook 5 min., stirring frequently.
Return meat to skillet; cook and stir 3 min. or until done. Remove from heat. Stir in 1/4 cup barbecue sauce mixture and nuts.
Spread remaining barbecue sauce mixture onto tortillas. Top with meat mixture; roll up.