Combine the sauce ingredients in a small bowl and set it aside. In another small bowl, mix the slurry ingredients thoroughly.
In a large skillet, heat 1/4 cup of water over medium-high heat until it’s hot. Once the water reaches a boil, add the broccoli and sprinkle it with a pinch of salt. Cover the skillet and let the broccoli steam for 1 minute. Afterward, uncover the pan and stir until the broccoli is al dente and the water has evaporated. Transfer the broccoli to a large plate.
Wipe the pan clean with paper towels and add 2 tablespoons of oil. Increase the heat to high. Add the mushrooms and let them sear for 1 minute without moving them. Then, flip the mushrooms and cook, stirring occasionally, for 2 to 3 minutes, until they are browned and no juice remains in the pan.
Push the mushrooms to one side of the pan. Pour the remaining 1/2 tablespoon of oil on the other side, then add the chili peppers, garlic, ginger, and green onions. Stir a few times until the chili peppers turn dark red, then mix everything together.
Return the broccoli to the pan and pour in the sauce. Stir and cook for 30 seconds. Give the slurry mixture another stir to ensure the cornstarch is fully dissolved, then swirl it into the pan. Cook and stir until the sauce thickens, then transfer everything to a large plate. Serve hot as a side dish or over steamed rice as a main course.