In a large bowl, add pork, cabbage, mushrooms, scallions, soy sauce, cornstarch, ginger, sesame oil, mirin, garlic, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Mix well to combine (I like to use my hands while wearing gloves, but a sturdy spatula works too). You will have about 3 cups of filling.
To test the seasonings in your filling (and important step to be sure it is properly seasoned), scoop a teaspoon-sized ball of filling, flatten into a patty, and fry in a dry skillet until browned, about 2 minutes per side. Taste and add more salt and pepper if desired (I usually add another 1/2 teaspoon salt and 1/4 teaspoon pepper, or 1 teaspoon salt and 1/2 teaspoon pepper total). Fry a second teaspoon of filling if you want to double-check your seasonings.
On a clean work surface, arrange 8 wonton wrappers (keep remaining wrappers covered with a damp kitchen towel or paper towel to prevent them from drying out). Brush the edges of each wonton wrapper with water.
Place 1 tablespoon filling in the center of the wrapper (I like to use the OXO small scoop, a #70 portion scoop). Fold the wrapper in half to enclose the filling, and pleat the outer edge, pressing damp edges together firmly. Transfer to a plate under the damp kitchen towel while preparing the rest of the potstickers.
In a large nonstick frying pan over medium-high heat, heat 1 tablespoon oil until shimmering. Add 12 pot stickers, flat bottom down and in a single layer. Sear until golden brown on the bottom, 2 to 3 minutes.
Pour 1/4 cup broth in the pan, cover, and let steam until all the broth evaporates, the pot stickers are tender but still firm, and the filling is cooked through, 3 to 4 minutes. Cook the remaining pot stickers and broth in three more batches. Serve with the ginger sauce.