In a large saute pan or wok, swirl in 1 tablespoon of the cooking oil. Turn on the heat to medium-high and immediately add garlic, ginger and green onion, stirring frequently. By the time the oil is hot, add the mushrooms, cabbage, carrots and bamboo shoots.
Turn heat to high and stir-fry the vegetables for about 2 minutes. and then toss in the bean sprouts. Add in the soy sauce and sesame oil. Cook for another minute. Then spread the filling out onto a large baking sheet. Prop the baking sheet up on one side to allow any juices to accumulate at the bottom (and discard to juices)
In a small bowl, whisk together the cornstarch and 1/4 cup of cool water to form a slurry.
Place a wonton or spring roll wrapper on a flat surface, add 1 tablespoon of the vegetable mixture into a corner of the wrapper, and then roll the edge of the wrapper tightly around the mixture. Fold the two side corners towards the middle of the wrapper while continuing to roll up. Paint the top edge with the cornstarch slurry mixture and wrap tightly the rest of the way. Make sure all edges are tightly sealed. Place seam side down. Cover with plastic wrap to avoid drying out.
In a large wok or medium saucepan over high heat, add about 1-2 inches of cooking oil.
Slide several egg rolls into the oil and allow them to cook for 2-3 minutes, turning them over a couple times, or until the wonton wrappers are golden brown. Remove the egg rolls to a cooling rack or paper-towel-covered plate to allow them to drain. Serve hot.