To make the filling, combine the ingredients for the ground pork together. Marinate at least 10 minutes.
In the meantime, shred the cabbage and the carrots using your food processor or by hand. Slice the mushrooms into very thin strips (or you could use your food processor and pulse a few times to get a fine dice.
Heat a wok or large sauté pan over high heat. Add the cooking oil and swirl to coat. Add the pork and stir-fry until no longer pink, about 2-3 minutes. Turn the heat to medium-low and push the meat to one side of the pan.
Add the shredded veggies and stir-fry for 1 minute, until the vegetables are softened.
Add the rice wine vinegar, soy sauce, sugar, sesame oil and black pepper. Continue to stir-fry for another minute.
Scoop the filling out of the wok and place on a baking sheet and spread out to cool. Prop up one end of the baking sheet so that it tilts and allows all the moisture to drain to one end. Let cool for at least 15 minutes.
Discard all of the accumulated juices. Use some paper towels to blot the filling to absorb any extra oil or juice.
Now, you're ready to wrap; IMPORTANT: Use only 1 heaping tablespoon of filling for each egg roll. These are slender egg rolls, the width of the egg roll should only be 1.25" diameter. Too much filling and the egg rolls may split open letting oil into the filling.
Lay the wrapper on a clean, dry surface so that it looks like a diamond (not a square). Spoon just a heaping tablespoon of filling near the bottom corner.
Lift the bottom corner up and over the filling and roll until you reach halfway. Fold over the left side corner, and then the right side corner towards the center.
Continue rolling and tucking as you go to keep it tight. Dip your finger into the egg/water mix and brush on the final top corner. Finish up the roll and seal.
Keep the rolled egg rolls in neat, single layer and cover with plastic wrap to prevent them from drying out. If you want to stack the egg rolls, make sure you have layer of parchment or wax paper in between the layers to prevent sticking. Refrigerate for up to 4 hours until ready to fry or freeze.
To fry the egg rolls, fill a wok or pot with at least 2 inches of high-heat cooking oil. Heat the oil to 350°F. Gently slide in or lower the egg rolls, frying 4 to 6 at a time, turning occasionally until golden brown (about 1½ minutes).
Place on a wire rack to drain. If needed, hold in a 150°F oven to keep warm and crisp.
Serve warm with dipping sauces.
Freeze egg rolls stacked on a plate with wax paper in between; when done place frozen egg rolls in quart freezer bags. To fry frozen egg rolls, do not defrost (they will get soggy), just add them to the oil frozen, frying 4 to 6 at a time. Add an additional 1½ minutes to the frying time since they are frozen.