Fresh vegetables and shrimp are sauteed, then quickly cooked in a mushroom-hoisin sauce. This savory combination becomes the filling for a reduced-fat omelet, which is cooked by swirling the egg mixture in the heated wok.
Place the shiitake mushrooms in a small bowl, add 3/4 cup boiling water, and let sit 30 minutes. Strain; cut the mushrooms into 1/4-inch slices. Set aside. Pour the liquid through a coffee filter to strain; set aside. Place the eggs, egg whites, salt, and pepper in a medium bowl, and whisk to combine. Divide egg mixture evenly between 2 small bowls, and set aside.
Place the wok over high heat. Add 1/2 teaspoon sesame oil. When hot, add the shrimp, and cook, stirring frequently, until bright pink and just cooked, 2 to 3 minutes. Remove from wok, and place in a small bowl. Add the remaining 1/2 teaspoon sesame oil to the wok. Add the onion and garlic, and cook, stirring constantly until the onion is translucent, about 3 minutes. Add the carrot and red pepper, and cook, stirring frequently, until just tender, about 4 minutes. Add the reserved soaked mushrooms, reserved shrimp, snow peas, and bean shoots, and stir to combine.
Push the vegetables and shrimp to the sides of the wok. Add the reserved mushroom-soaking liquid, hoisin sauce, low-sodium soy sauce, cornstarch mixture, ginger, and chile to the center of the wok, and stir until combined and slightly thickened, about 2 minutes. Combine sauce with the vegetables and shrimp. Transfer vegetable-and-shrimp mixture to a bowl, and cover to keep warm.
Wipe out the wok, and return to high heat. Add canola oil, and swirl to coat wok. Pour half the egg mixture into the wok; swirl so the egg mixture coats the wok creating an omelet of even thickness, about 10 inches in diameter. Continue to swirl as the egg cooks, about 3 minutes. Once the omelet is completely set and browned on the bottom, use a spatula to loosen it, and slide it onto a plate. Cover to keep warm. Repeat the process with the remaining egg mixture to make a second omelet. Add half the reserved vegetable-and-shrimp mixture to half of each omelet; fold the omelets to cover the vegetable-and-shrimp mixture. Cut omelets in half, and transfer them to serving plates; garnish with snow-pea shoots if desired.