Preheat the oven to 425 degrees F (220 degrees C). Brush a large baking pan with 1/2 teaspoon vegetable oil and set aside.
Heat sesame oil in a large skillet over medium-high heat. Add garlic and ginger and saute, 1 to 2 minutes. Add cooked chicken, cabbage, carrot, soy sauce, and dry garlic sauce. Cook and stir until vegetables are soft, 2 to 3 minutes. Mix in cooked rice. Keep on low heat while preparing the rice papers.
Wet a cloth with warm water and place one rice paper sheet inside. Wrap completely and let soften, about 1 minute. Add 1/4 cup of the chicken mixture to the middle of the rice paper sheet. Fold both ends in and roll from one side to the other. Place wrapped roll onto the prepared baking sheet.
Repeat the wetting, filling, and wrapping process to make remaining rice paper rolls. Brush rolls with remaining vegetable oil.
Bake in the preheated oven for 10 minutes, then turn over to bake for an additional 10 minutes.