Gyoza

Heat sesame oil in a large skillet over medium-high heat. Add cabbage, onion, carrot, and garlic; cook and stir until cabbage is limp, 3 to 4 minutes. Add ground pork and egg; cook and stir until pork is browned and crumbly, 5 to 7 minutes.

Make the gyoza: Place about 1 tablespoon pork mixture into the center of a wonton wrapper. Fold wrapper in half over filling, then seal the edges with moistened fingers. Repeat to make remaining gyoza.

Heat vegetable oil in a large skillet over medium-high heat. Cook gyoza in the hot skillet until lightly browned, about 1 minute per side. Add water to the skillet, reduce the heat, cover, and steam gyoza until water is gone. Remove from the heat.