Heat oil in a skillet or wok over high heat. Add the garlic, ginger, and scallions and cook for 1 minute. Add the mushrooms and cook for another minute.
Add the cabbage and carrot and cook until the cabbage starts to wilt, about 2 minutes.
Stir in the hoisin and oyster sauces; toss to coat the mixture.
Remove from the heat and mix in the noodles, sprouts, and cilantro; season to taste with salt and pepper. The filling should be moist but not wet. Remove from heat and allow to cool.
Lay a spring roll wrapper on a flat surface on an angle so it looks like a diamond. Spoon 2 tablespoons of the filling near the bottom corner of the wrapper and fold up to enclose the filling. Fold in the 2 sides. Paint the top seam of the wrapper with beaten egg. Continue rolling up to form a tight cylinder.
Pour about 1-inch of oil in a skillet or wok and heat to 350 degrees F. Fry the spring rolls, turning to cook all sides, until browned, about 2 minutes. Drain on paper towels and keep warm. Serve with Mustard Dipping Sauce.
For the Mustard Sauce: Mix all ingredients together and stir until the sugar dissolves.