In a large mixing bowl, combine the finely chopped cabbage, grated carrots, chopped green onions, minced garlic, soy sauce, sesame oil, salt, and pepper. Mix everything until well incorporated to ensure each dumpling is packed with flavor.

Take a dumpling wrapper and place about a tablespoon of the filling in the center. Moisten the edges of the wrapper with a little water. Fold the wrapper in half, pinching to seal, and ensure there are no air bubbles.

Heat a large skillet over medium-high heat and add enough oil to coat the bottom. Once hot, place the dumplings in a single layer in the skillet. Fry for about 2-3 minutes, or until the bottoms are golden brown.

Carefully add a splash of water to the pan, then quickly cover with a lid. Allow the dumplings to steam for approximately 5-6 minutes, until they are cooked through.

Remove the lid and let any remaining water evaporate. Transfer the dumplings to a serving plate and enjoy them hot with your choice of dipping sauce.