Add diced cabbage to a fine mesh sieve and toss with ½ teaspoon salt. Place over a bowl and let sit for 20-30 minutes then press cabbage down with a rubber spatula quite a few times to squeeze out excess moisture. Set aside.
Add egg yolk to a large bowl and whisk. Add all remaining filling ingredients (including the cabbage) and mix with your hands until thoroughly combined.
Assemble
Line a baking tray with parchment paper and prepare some damp paper towels or a damp cloth. Keep all the wrappers covered with plastic wrap when you are not using them. Fill a small bowl with water.
Working with 2-4 wrappers at a time (depending on how fast you are), add 1 tablespoon to the middle of each wrapper. Dip your finger in water and run it around the edge of half of the wrapper. Fold the wrapper over in half to create a half-moon shape and pinch the edges firmly together to seal. Place filled wrappers on the prepared baking tray and cover with damp paper towels/cloth. Repeat with the remaining wrappers.
Cook
Heat 1 tablespoon of oil in a large skillet (that has a lid) over medium-high heat. Add about 12 gyoza to the skillet flat side down - enough that will comfortably fit without overcrowding. Cook without touching the potstickers until the underside is lightly golden, approximately 2 minutes.
Stand back and use one hand to hold the lid as a shield as you pour 1/3 cup of water around the potstickers, then quickly place the lid on. Turn the heat to LOW and cook until water has completely evaporated. Remove the lid, increase heat to medium, and cook for 1-2 more minutes to crisp up the bottoms.
Transfer potstickers to a paper towel-lined plate or baking tray. Repeat until all potstickers are cooked. Served warm with the dipping sauce of your choice.
Notes
Gyoza wrappers are round wrappers located in the refrigerated section. If your grocery store doesn’t have them, then you should be able to find them at your local Asian Market. Locally, we have Twin Dragon brand potstickers/gyoza wrappers. In a pinch, you can use wonton wrappers. Just be careful, as wonton wrappers are a little thinner, and you may need to cut them into circles since most come in a square shape.