In a large bowl, combine ground beef, ketchup, mustard, Worchestire sauce, cornstarch, green onion, and salt and pepper.
Fill each gyoza wrapper in the center with about a 1 tablespoon of the mixture.
Add some cheese on top of the mixture, wet the edges with a little bit of water, and close to seal by pleating.
Heat a nonstick skillet to medium-high heat.
Drizzle a little vegetable oil.
Place the pot stickers with the flat side down.
Once the bottoms are golden brown, pour about 1/2 cup of water into the skillet and immediately cover.
When the wrapper has become slightly translucent, remove the lid and allow the water to evaporate.
Once the pot stickers are crispy, remove and place bottom side up on a plate.
Serve with ketchup and mayo for dipping.