Preheat Blackstone griddle to medium heat. Drizzle vegetable oil then add the coleslaw mix and mushrooms. Lightly season with salt and cook until tender for 10 minutes.
Remove mushrooms and coleslaw mix from the griddle and place into a large mixing bowl. Add the remaining gyoza ingredients except for the wrappers. Mix well until fully incorporated.
Lay the gyoza wrappers out on a large table. Evenly divide the filling between the wrappers. Spread the filling to the edges of the wrappers.
Lay the gyozas down on the griddle meat side down. Cook for 5 minutes until crispy. Flip the gyozas and cook for an additional 3-4 minutes until the underside is crispy. Remove from the griddle.
Combine all of the sauce ingredients in a bowl and quickly whisk. Serve alongside the gyozas.