Heat a large skillet over medium-high heat. Cook the ground chicken for 5 to 7 minutes, crumbling it into very small pieces until completely browned.
Add the minced garlic and grated ginger to the chicken. Sauté for 1 minute, until fragrant.
Add the bag of coleslaw mix to the skillet. Add the soy sauce, toasted sesame oil, and black pepper. Stir frequently for 3 to 4 minutes until the cabbage is slightly wilted.
Pour the entire meat and vegetable mixture into a fine mesh strainer over a bowl. Allow to drain and cool for at least 15 minutes. (Don’t skip this step!)
Lay an egg roll wrapper on a clean surface in the shape of a diamond. Cover remaining wrappers with a damp paper towel.
Spread 2 heaping tablespoons of filling in a horizontal line across the bottom third of the egg roll wrapper.
Bring the bottom point of the egg roll wrapper up over the filling, tightly. Fold both sides firmly to the middle, forming an envelope shape. Roll upward toward the top point.
Rub a finger in the water or beaten egg and run it along the top point of the wrapper. Firmly press down to close the egg roll. Repeat with remaining filling.
Heat the vegetable oil in a heavy bottomed pot to 350°F.
In small batches of 3 or 4, fry the egg rolls for 4 to 5 minutes, turning occasionally, until golden brown and crispy.
Transfer the fried egg rolls to a wire rack lined with paper towels and allow them to drain. Serve immediately with your favorite dipping sauce.