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1
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.
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2
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.
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3
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.
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4
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.
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5
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.
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6
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.
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7
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.
