Step 1In a medium bowl, lightly salt the chopped cabbage and toss to mix well, then set aside for 15 minutes. In batches, place the cabbage on a clean kitchen towel and wring the towel over the sink to squeeze out excess moisture. Set aside.
Step 2In the bowl of a food processor, place the duck, green onions, one-fourth teaspoon salt, ginger, garlic, sake and miso. Pulse just until the mixture becomes a coarse paste. Transfer to a mixing bowl and fold in the reserved cabbage and the garlic chives, mixing well.
Step 3To assemble the gyoza, place a wonton skin in the palm of one hand. Spoon 2 teaspoons of the gyoza mixture onto the center of the wonton skin. With your finger, wet the wonton skin's edges with the cornstarch-water mixture. Fold the skin in half and pinch it together, pressing out the extra air before sealing the skin. (The cornstarch will "glue" the wonton skin together.)
Step 4Place the gyoza on a plate and repeat with the rest of the mixture, which will make about 25 pieces. Keep the wonton skins covered with a moist paper towel while you work, so they don't dry out. Set the gyoza aside.
Step 1To make the dipping sauce, combine the soy sauce, rice vinegar, chile oil and green onions in a small bowl. Set aside.
Step 1In the bottom of a pot (such as a Japanese clay donabe or cast-iron Dutch oven), place the konbu. Add the chicken broth, sake and salt, and bring to a boil over high heat. Remove the konbu and discard. Reduce the heat to a simmer and add the nappa cabbage, negi, shiitake mushrooms and enoki mushrooms and cook for 2 minutes. Add the gyoza to the hot pot, making sure they're submerged in the broth. Continue to simmer until the gyoza are cooked through, 5 to 10 minutes (check by opening one up at the 5-minute mark). Add the spinach and simmer for 1 minute more.
Step 2While the hot pot simmers, fill four small bowls with the dipping sauce. Transfer the hot pot to the dining table. Dip the ingredients into the sauce-filled bowls, and eat. Add more dipping sauce to the bowls as needed.
Step 3Alternatively, this can be cooked tableside with a portable gas burner: Arrange the ingredients on serving platters. After preparing the gyoza and dipping sauce, do all the cooking at the dining table. Add the supporting ingredients all at once, or reserve half or more to cook later. Cook a few of the gyoza at a time.