"In our family, we make a meal out of gyoza about once a week. Just take them from the freezer and pop them into a frying pan, steam some rice, and your meal is ready. I make up a big batch and freeze them, and you may adjust the recipe size according to what you have on hand. Be prepared for those accounting fights about who gets the last gyoza. Mmmm! Enjoy with rice on the side sprinkled with some ground sesame seeds."
Cook pork in a skillet over medium heat, breaking up the meat with a wooden spoon, until no longer pink in the center, 8 to 10 minutes. Drain excess grease and transfer to a bowl.
Heat 1 tablespoon vegetable oil in the same skillet. Add onions; cook and stir until slightly softened and translucent, about 5 minutes. Season with salt. Add carrots; cook and stir until softened, 6 to 8 minutes. Add to the cooked pork.
Cook cabbage in the same skillet over medium-high heat, adding the pork-carrot mixture in gradually, until wilted, 6 to 8 minutes. Stir in vinegar, ginger, grape jelly, teriyaki sauce, 1 tablespoon soy sauce, 1 tablespoon oyster sauce, and sesame oil. Cook and stir gyoza filling until flavors combine, about 3 minutes.
Combine 1 tablespoon water and cornstarch in a small bowl. Add to the gyoza filling. Cook and stir until thickened, 3 to 5 minutes. Let cool, at least 20 minutes.
Place a dab of filling in the center of a dumpling wrapper. Fold over to form a semicircle and seal the circle edge with water; press firmly. Place gyoza on a baking sheet. Repeat with the remaining filling and wrappers.
Combine 1/2 cup water, rice wine vinegar, 1 1/2 teaspoons soy sauce, and 1 1/2 teaspoons oysters sauce in a bowl to make sauce.
Heat 1 tablespoon oil in a skillet over medium heat. Add gyoza in batches; cook until browned, 4 to 5 minutes. Add some of the sauce. Cook, covered, until liquid is absorbed, about 5 minutes. Repeat with remaining gyoza and sauce.