Lumpia is the Phillipino version of a Chinese egg roll. The skins used, though, are light and flaky instead of doughy. They are similar to a Vietnamese spring roll but more loaded with meat, and very skinny. They are addicting and easy to eat; you can make a bunch ahead and freeze them either before or after frying.
In a food processor, chop the garlic as small as possible. Add the green onion and yellow onion and pulse to a similar size as the garlic. Add and pulse the shiitake mushroom caps and water chestnuts until all are a similar size. Add the shrimp and pulse until the shrimp are a coarse hamburger grind. Add the ground pork, soy sauce, fish sauce, brown sugar and pepper and mix all thoroughly. Transfer to a bowl, then cover with plastic wrap and refrigerate for 30 minutes.
Preheat 1 inch frying oil to 350 to 360 degrees F in a heavy-bottomed pot.
Carefully peel one wrapper off the stack. Orient the wrapper square to the edge of the counter, not diagonal. Scoop about a heaping tablespoon (approximately 1 ounce) of the filling and spread it about an inch from the edge closest to you and about 1/2 inch from each side. Brush all of the edges with the egg wash. Fold the edges in on the sides and begin rolling the bottom of the wrapper to the top, making a tight rope. Make sure when you finish rolling that the egg wash has sealed the roll. Place the lumpia seam-side down on a plate while you make the remaining lumpia. (This amount of filling should make approximately 30 rolls. (These could be made smaller for appetizers.)
Fry in batches until golden brown and cooked through, about 3 minutes. Remove to drain on a rack or paper towels. Serve hot with sweet chile sauce mixed with vinegar to taste.