Prepare the sauce: In a small bowl, stir together the soy sauce, cooking wine, bean paste, mushroom seasoning, white pepper, and cornstarch with 2 tablespoons water.
Prepare the mushrooms: Gently pound the mushrooms with a pestle or the bottom of a small jar to break them open. Tear them into 1/2-inch (12 mm) strips. For thicker mushrooms, cut them into 2-inch (5 cm) sections before pounding for easier tearing.
Heat a dry large skillet or nonstick pan over medium-low heat. Stir-fry the mushroom strips for about 5 minutes, until they release their moisture. Transfer to a large bowl.
Add the cooking wine, soy sauce, white pepper, and salt to the mushrooms. Sprinkle on the cornstarch, then toss with your fingers (or chopsticks) to evenly coat the mushrooms in starch.
Fry the mushrooms: In the same skillet, heat 1 tablespoon of the oil over medium-high heat. Add the mushrooms and stir-fry until they're golden brown and slightly crispy, 4 to 5 minutes. Remove to a plate.
Stir-fry the aromatics: Heat the remaining 1 tablespoon oil in the pan over medium-high heat. Sauté the ginger and garlic until fragrant, about 30 seconds. Add the chiles and cook briefly to remove their raw taste, about 30 seconds.
Finish and serve: Return the fried mushrooms to the pan, pour in the prepared sauce, and stir-fry until the mushrooms absorb all the sauce, about 2 minutes. Serve warm with rice.