In a medium bowl, combine pork, soy sauce, cornstarch, sugar, and pepper. Allow to marinate for at least 10 minutes.
Shred or thinly slice the cabbage, carrots, and mushrooms.
In a large wok or pan, drizzle 1 tablespoon vegetable oil over medium high heat. Add the pork and cook, breaking up into small pieces, until browned, about 3 minutes. Push the pork to the side of the pan and reduce heat to medium low. Add the cabbage, carrots, mushrooms, garlic, and ginger to empty side of pan. Cook, stirring constantly, until vegetables begin to soften. Stir in the rice wine, soy sauce, sesame oil, salt, sugar, and pepper. Cook for a minute, then remove from heat.
Slightly prop a large baking sheet, placing paper towels under the lower end to catch any excess moisture. Spread the filling out on the baking sheet to cool. Once filling has cooled, use a paper towel to press out any excess moisture.
Place the egg roll wrappers next to work surface and cover with a towel to keep from drying. In a small bowl, mix together water and cornstarch.
Place wrapper on a dry work surface with corner facing you. Place a heaping tablespoon of cooled filling in a line above the nearest corner. Starting from that corner, tightly roll up halfway, then tuck in the sides. Wet the top edge with the cornstarch water, then continue rolling to seal. Place on a large baking sheet lined with parchment with the seam side down. Repeat with remaining wrappers and filling. Cover the prepared egg rolls on baking sheet with towel.
To try, pour oil into wok until 2 inches deep over medium heat. Once 350 degrees F, gently add a few egg rolls. Don't overcrowd. Fry on each side until golden brown, about 1 1/2 minutes per side. Place on towel lined plate or wire rack to cool slightly. Repeat with remaining egg rolls.