Heat olive oil in a large skillet over medium heat. Add chopped onion and sauté until translucent, about 2-3 minutes.

Add ground chicken to the skillet and cook, breaking it apart with a spatula, until it's no longer pink, about 5-7 minutes.

Stir in minced garlic, minced ginger, kosher salt, and black pepper. Cook for an additional 2 minutes, until fragrant.

Add sesame oil, shredded cabbage, shredded carrots, and sliced green onions to the skillet. Cook for 2-3 minutes, until the vegetables are slightly softened. Remove from heat and let the filling cool slightly.

Take one egg roll wrapper and place it on a clean surface in a diamond shape, with one corner pointing towards you.

Spoon about 2 tablespoons of the chicken and vegetable filling onto the center of the wrapper.

Fold the bottom corner of the wrapper over the filling, then fold in the side corners towards the center. Roll tightly, keeping the filling secure, and brush the top corner with the beaten egg to seal the egg roll.

Repeat with the remaining wrappers and filling until all egg rolls are assembled.

In a large pot or deep fryer, heat vegetable oil to 350°F.

Carefully place the egg rolls in the hot oil, in batches if necessary, and fry until they are golden brown and crispy about 3-4 minutes.

Once done, remove the egg rolls from the oil using a slotted spoon and drain on a paper towel-lined plate to remove excess oil.

Serve the chicken egg rolls hot with your favorite dipping sauce, such as sweet chili sauce or soy sauce.