Whisk together sauce ingredients and set aside.
Heat 2 teaspoons vegetable oil in large skillet, wok, or stockpot over medium-high. Add potstickers folded side up. Cook for 3 minutes, unmoved, until browned on bottoms.
Slowly pour in water and add lid. Cook in water for 3 more minutes. Remove potstickers from pan and set aside in large bowl.
In same pan heat half teaspoon oil over medium-high and add mushrooms. Season with salt and pepper and cook for 5 minutes. Add mushrooms to bowl with potstickers.
In same pan add remaining oil and heat over medium-high. Add asparagus and carrot and cook for 2-3 minutes or until tender. Add ginger and cook for 1 minute. Add salt to taste. Turn off heat.
Add sauce, potstickers, and mushrooms to pan and stir well. Let sit in pan for 1 minute. Stir in green onions and serve piping hot.
