In a small bowl, whisk together cold water and cornstarch to create a slurry. Add soy sauce, rice wine vinegar, sugar or honey, and grated ginger. Whisk until well combined and set aside.

Slice the carrot thinly on a bias. Slice the mushrooms and green beans into thirds. Cut the broccoli into small florets. Dice the onion.

Heat 1 tablespoon olive oil and 1 tablespoon sesame oil in a large skillet over medium-high heat. Add frozen potstickers in a single layer. Fry until the bottoms turn brown, about 3 to 4 minutes.

Add 2 tablespoons of water to the skillet, cover, and cook for an additional 3 to 4 minutes. Remove potstickers from the skillet and set aside.

In the same skillet, add 1 tablespoon of olive oil. Add sliced mushrooms and diced onion. Cook until mushrooms are browned, about 3 to 4 minutes. Remove from the skillet and set aside.

Add 1 teaspoon of sesame oil to the skillet. Add broccoli florets and cook for 3 to 4 minutes until tender. Remove from the skillet and set aside.

Add 1 tablespoon of olive oil to the skillet. Add sliced green beans and carrots. Cook for 3 to 4 minutes until vegetables are tender but still crisp.

Add the cooked broccoli, mushrooms, and onions back into the skillet. Stir to combine.

Add the cooked potstickers to the skillet. Pour the prepared sauce over the mixture. Stir gently to coat everything evenly. Cook for an additional 2 to 3 minutes until the sauce thickens.

Transfer to a serving dish and garnish with sesame seeds and sliced green onions. Serve with rice.