Place mushrooms, carrot, garlic, ginger, broth and soy sauce in a 6-quart slow cooker. Cover and cook on low for 4 hours until the mushrooms and carrot are tender.
Turn the cooker to high, cover and heat for 15 minutes until the broth is very hot.
Add frozen fully cooked potstickers and napa cabbage, pressing them gently into the liquid. Cover and cook on high for 15 to 25 minutes until the dumpling centers reach 165°F, following any longer package heating requirement.
Stir in rice vinegar, sesame oil and scallions carefully without tearing the wrappers.
Lift 6 potstickers into each of 4 bowls with a slotted spoon, then ladle over the broth and vegetables and serve immediately.