Combine the vegetable broth, light soy sauce, dark soy sauce, sugar, black pepper, and sesame oil in a small bowl. Stir well and set aside. In a separate bowl, mix the cornstarch with 2 tablespoons of water until smooth and set aside.

Heat 1/4 cup water in a large skillet or wok over medium-high heat. Once the water starts boiling, add the broccoli florets and sprinkle with a pinch of salt. Cover the pan and steam for 1 minute. Remove the lid and stir for 1-2 minutes until the broccoli turns bright green and tender-crisp. Continue stirring until all water has evaporated from the pan. Transfer to a plate.

Wipe the pan clean with paper towels and add 2 tablespoons of peanut oil. Turn the heat to high and wait until you see the oil shimmer (about 30 seconds). Add the sliced mushrooms in a single layer. Let them sear undisturbed for 1 minute to develop a golden crust. Flip and cook for another 2-3 minutes, stirring occasionally, until deeply browned and all moisture has cooked off.

Push the mushrooms to one side of the pan. Add the remaining 1/2 tablespoon of oil to the empty side, then add the dried chili peppers, minced garlic, minced ginger, and sliced green onions. Stir these aromatics for about 30 seconds until the chili peppers darken to a deep red and the garlic turns golden. Mix everything together with the mushrooms.

Return the broccoli to the pan and pour in the prepared sauce. Stir everything together for 30 seconds. Give the cornstarch slurry a quick stir to make sure it's completely dissolved, then swirl it into the pan. Cook and stir for 30-60 seconds until the sauce thickens and coats the back of your spoon with a glossy sheen. Serve hot over steamed rice or as a side dish.