Add the carrots, onion, cabbage, garlic, and ginger to a non-stick pan over medium high heat with enough broth to keep from sticking. Cook for about 6 minutes, stirring often, until the cabbage and carrots begin to soften.

Once they begin to soften, add in the mushrooms, green onion, and tofu (if adding) and cook until mushrooms are soft. Whisk the cornstarch with 1/4 cup vegetable broth and add to the pan along with the sesame oil and soy sauce.. Stir over the heat until it thickens. Remove from heat and season with pepper and salt to taste.

To assemble, rub edges of wrapper with water and spoon about 1 tablespoon of filling onto center. Fold edges together and pinch to seal. Repeat with all potstickers.

In a clean non-stick pan, lay about half the potstickers flat on one side and place over medium high heat. Cook for about 2 minutes to allow bottoms to brown, then pour in about 1 cup water (enough to cover them halfway). Cover with a lid mostly on to allow steam to escape and cook for 5 to 8 minutes until water has evaporated.