Stir together coleslaw mix; meat, poultry, or shrimp; ginger; pressed garlic; pepper; and salt.
Brush water around outer edge of each egg roll wrapper. Spoon 1/3 cup filling mixture in center of each wrapper. Fold bottom corner over filling, tucking tip of corner under filling; fold left and right corners over filling. Tightly roll filled end toward remaining corner; gently press to seal.
Pour oil to a depth of 3 inches in a Dutch oven; heat to 375°. Fry egg rolls, in batches, 3 to 4 minutes or until golden brown; drain on paper towels. Serve immediately with desired condiments.