Making Pan-Fried Cabbage and Noodle Buns is straightforward. Just follow these simple steps:

1. Prepare the Cabbage: In a large skillet, heat 1 tablespoon of vegetable oil over medium heat. Add the sliced cabbage and cook until tender, approximately 5-7 minutes.
2. Add Flavors: Stir in minced garlic, soy sauce, sesame oil, salt, and black pepper. Cook for an additional 2-3 minutes until fragrant. Remove from heat and let cool slightly.
3. Mix in Noodles: In a large bowl, combine the cooked noodles with the cabbage mixture. Mix well to ensure the flavors are evenly distributed.
4. Assemble the Buns: Place a dumpling wrapper on a clean surface. Add about 1-2 tablespoons of the filling mix in the center of each wrapper.
5. Seal the Buns: Wet the edges of the wrapper with water. Fold it in half to create a half-moon shape and pinch the edges to seal tightly. Repeat this process for the remaining wrappers and filling.
6. Pan-Fry the Buns: In the same skillet, add the remaining vegetable oil and heat over medium-high. Place the buns in a single layer and cook until golden brown, approximately 3-4 minutes per side.
7. Steam the Buns: Once the buns are golden, add ¼ cup of water to the skillet and cover immediately. Allow to steam for 5-7 minutes until the buns are cooked through.
8. Serve: Carefully remove the buns from the skillet and let them rest for a minute before serving.

By following these steps, your Pan-Fried Cabbage and Noodle Buns will turn out deliciously, showcasing a perfect blend of textures and flavors.