In a large skillet, heat 1 tablespoon vegetable oil over medium heat.
Add minced garlic and grated ginger to the skillet and sauté for 30 seconds until fragrant.
Add ground chicken to the skillet and cook, breaking it apart with a spatula, until fully cooked and no longer pink, about 5-6 minutes.
Stir in shredded cabbage, shredded carrots, and chopped green onions. Cook for 3-4 minutes until vegetables are tender.
Add soy sauce, sesame oil, ground black pepper, and salt to the mixture. Stir well to combine and cook for another 1-2 minutes.
Remove the skillet from heat and let the filling cool slightly.
In a small bowl, mix cornstarch and water to create a slurry. This will be used as glue for sealing the spring rolls.
Place one spring roll wrapper on a clean flat surface with one corner pointing toward you (diamond shape).
Spoon about 2-3 tablespoons of the chicken filling near the corner closest to you.
Fold the corner over the filling, then fold in the two side corners towards the center.
Roll the wrapper tightly toward the far corner, brushing the edge with the cornstarch slurry to seal the spring roll.
Repeat the rolling process with the remaining wrappers and filling.
Heat 1 cup vegetable oil in a deep skillet or frying pan over medium-high heat until hot but not smoking (about 350°F or 175°C).
Carefully add 2-3 spring rolls at a time to the hot oil, frying for 3-4 minutes, turning occasionally, until golden brown and crispy.
Remove the spring rolls with a slotted spoon and drain on paper towels.
Serve the crispy chicken spring rolls hot with your favorite dipping sauce.