Place mushrooms and vermicelli in 2 separate bowls with lukewarm water to cover. Let soak until softened, at least 15 minutes. Drain mushrooms and chop into small cubes. Drain vermicelli.
Heat 1 to 2 teaspoons vegetable oil in a wok over medium-high heat. Add duck; cook, stirring continuously, until golden brown, about 5 minutes. Season with salt and pepper. Transfer duck to a bowl.
Heat about 3 inches vegetable oil in a medium-large pot to 350 degrees F (175 degrees C). Add vermicelli; fry until fritters are crisp and crunchy but not golden brown, 2 to 3 minutes.
Pour the remaining vegetable oil into the wok over medium heat. Add mushrooms; cook and stir until soft, 4 to 5 minutes. Return duck to the wok; cook until heated through, about 2 minutes.
Place vermicelli fritters on a large plate; pour the duck stir-fry on top. To eat, drizzle hoisin sauce on a piece of lettuce; spoon the duck and vermicelli stir fry on top. Hold the lettuce wrap together with your fingers.
Chinese black mushrooms are also called 'shiitake mushrooms.'
You can use vegetable, peanut, or corn oil for stir-frying and deep-frying. Do not use olive oil.
We have determined the nutritional value of oil for frying based on a retention value of 10% after cooking. Amount will vary depending on cooking time and temperature, ingredient density, and specific type of oil used.
Per Serving: 370 calories;20.4 g fat;
22.9 g carbohydrates;
24.2 g protein;
124 mg cholesterol;
217 mg sodium.