Finely dice the vegetables and place them in a large bowl with the rest of the filling ingredients. Mix until everything is evenly distributed.
Prepare a small bowl of water and a tray for the completed gyoza next to you. Place a wrapper on your palm and add about ½-1 tbsp of filling to the center, leaving a thick border. Lightly wet the border. Be careful not to overfill, add slightly less than you think.
Pinch two parallel edges together and push them to the middle so that the edges form a cross along the top.
Firmly pinch the edges together to seal them shut.
Fold down each edge in the same direction to create the windmill shape.
If there is a hole in the center, pinch it tightly to close it, then place it on the prepared tray.
Repeat until you've used up all of your wrappers and filling.
Preheat your oil to 170 °C (338 °F). Once hot, gently place the gyoza in the oil and fry for 2 minutes.
Flip them and fry for another 2 minutes, or until crispy and golden all over.
Rest on a wire rack to drain any excess oil.
Serve with ponzu or your choice of dipping sauce. Enjoy!
Notes
Seal the windmill fold with no gaps: Any open pleat or an unpinched hole in the center lets the filling push out and leak into the oil. Press each seam flat as you fold, and give the center point a final firm pinch before it fries.Keep the filling modest: Overpacked gyoza swell in the oil and shoulder the seam apart. Use less than feels right, keep each mound small and centered, and leave a clear dry border to pinch. A slightly underfilled gyoza fries up beautifully.Fry at a steady 170°C, not hotter: Too hot and the shell browns and sets before the middle cooks, leaving it golden outside and raw within. Hold a moderate 170°C (338°F) and give them the full couple of minutes per side.Bury the cheese in the center: Melted cheese turns more fluid than the meat and slips through any pinhole the filling would never pass. Keep it away from the seams, shred it fine, and fold with a cold, firm filling so it holds its place.Freeze raw, fry from frozen: To make ahead, freeze the folded gyoza raw on a tray, then bag them. Fry them straight from frozen with no thawing, knocking off loose frost first. Freezing after frying costs you the crunch.