Chop the vegetables into medium pieces, not too small, and place them in a large bowl. Add the soy sauce, balsamic vinegar, and a little vegetable oil, toss well, and let the vegetables marinate for a few hours.
Pour some vegetable oil into a preheated skillet. Add two garlic cloves crushed with the side of a knife, 2–3 slices of fresh ginger, a few pieces of green onion, and the star anise. Cook briefly until the oil is fragrant.
Once the oil is infused with the flavor and aroma of the ginger, garlic, and star anise, add the marinated vegetables to the skillet in an even layer.
Stir‑fry the vegetables over high heat for 5–7 minutes, stirring from time to time and watching that they do not burn. Taste and, if needed, add salt. Pour in a little water, reduce the heat to low, cover with a lid, and let the vegetables cook for another 5–10 minutes.
Some people like their vegetables crisp‑tender, while others prefer them soft, so cook them to your taste. When serving, sprinkle the vegetables with chopped green onion.