In a large skillet, heat 1 tablespoon of sesame oil over medium-high heat. Add the ground chicken and cook, breaking it apart with a spoon, until browned and cooked through, about 5-7 minutes. Drain any excess fat.

Add the minced garlic and grated ginger to the skillet with the chicken. Sauté for 1 minute until fragrant.

Stir in the coleslaw mix, bamboo shoots, and water chestnuts. Cook for another 5-7 minutes, stirring occasionally, until the vegetables have softened slightly and released most of their moisture. It's crucial not to overcook them as they will cook more when fried.

Stir in the soy sauce, oyster sauce (if using), sugar, and black pepper. Mix well to combine all ingredients. Remove the skillet from heat and let the filling cool completely. Cooling is important to prevent wrappers from becoming soggy.

Once cooled, stir in the sliced green onions.

Lay an egg roll wrapper on a clean, dry surface with one corner pointing towards you (diamond shape). Place about 2-3 tablespoons of the cooled chicken and vegetable filling slightly below the center of the wrapper.

Fold the bottom corner of the wrapper over the filling, tucking it in tightly. Roll it once, then fold in the left and right corners towards the center, creating an envelope shape.

Brush the remaining top corner of the wrapper with the beaten egg. Continue rolling the egg roll tightly from the bottom towards the top corner, sealing it firmly with the egg wash.

Repeat with the remaining wrappers and filling. Place the assembled egg rolls on a baking sheet lined with parchment paper, ensuring they don't touch each other.

In a deep fryer or a large, heavy-bottomed pot (like a Dutch oven), heat 4-6 cups of vegetable or peanut oil to 350°F (175°C). Use a candy thermometer to monitor the temperature accurately.

Carefully place 3-4 egg rolls into the hot oil, ensuring not to overcrowd the pot. Fry for 5-7 minutes, turning occasionally, until they are golden brown and crispy on all sides. The internal temperature of the filling should reach 165°F (74°C).

Using a slotted spoon or spider, remove the cooked egg rolls from the oil and transfer them to a wire rack lined with paper towels to drain excess oil. This helps keep them crispy.

Repeat with the remaining egg rolls, making sure the oil temperature returns to 350°F (175°C) before adding the next batch.

Serve the crispy chicken egg rolls hot with your favorite dipping sauce, such as sweet and sour sauce, duck sauce, or hot mustard.