Whisk together the sugar, soy sauce, and rice wine and then toss with the chicken or shrimp. While it sits, put 2 tablespoons of oil in a large skillet and turn the heat to medium-high. A minute later, add the mushrooms, scallions, and bean sprouts; cook, stirring occasionally, for about 3 minutes. Remove from the pan with a slotted spoon. Add another tablespoon of oil to the skillet and cook the ginger, stirring, until fragrant, about 30 seconds. Add the chicken or shrimp and its marinade and cook until it loses its pinkness, stirring occasionally to separate the pieces, about 3 minutes. Return the vegetables to the pan, mix well with the chicken or shrimp, and cook for another minute. Remove the mixture with a slotted spoon. (You can prepare this filling, covered and refrigerated, up to a day in advance.) Add at least 3 inches of oil to a heavy saucepan or deep- fryer (a narrow vessel will save you oil; a broad one will allow you to cook more egg rolls at once); heat over medium-high heat until it reaches about 350 degrees F. Meanwhile, moisten the edges of an egg roll wrapper with water and put 2 tablespoons of the filling down a line in the center; fold in the sides and roll tightly. Seal the seam with a few drops of water. Working in batches, place the egg rolls in the oil and turn occasionally to brown evenly; the cooking will be easy and quick, about 5 minutes per batch (you just have to heat them through and brown the outside; everything inside is already cooked). Adjust the heat as necessary so that the egg rolls brown evenly. As they finish, drain on paper towels. Serve hot, with any of the sauces.