Heat 2tbsp peanut or vegetable oil in a large sauté pan. Add grated ginger and garlic and cook until fragrant, about 30 seconds.
Next add onions, slit green chilies, carrot, broccoli and mushrooms. Cook on medium-high flame until the veggies start to turn lightly browned around the edges, about 3~4 minutes.
Add the broth and bring to a boil, lower the heat and cook until the veggies are fork tender.
In the meantime, whisk cornstarch with ½cup of water into a smooth slurry.
Once the veggies are done, add soy sauce, sugar, salt and pepper. Mix well and bring to a boil again.
Stir in the cornstarch slurry and cook until the gravy thickens.
Just before turning off, add toasted sesame oil and mix well. Serve hot over steamed rice. Enjoy!!