Prepare the vegetables and herbs. Finely chop the shiitake mushrooms and scallions, grate the ginger, and mince the garlic. Wash and gently pat dry the 16 shiso leaves; trim off tough stems. Keep the gyoza wrappers covered with a clean, slightly damp towel so they stay pliable. Finely chopped vegetables make it easier to seal the dumplings without tearing the wrappers.
Mix the pork filling. In a bowl, combine the cold ground pork, mushrooms, scallions, ginger, garlic, 2 teaspoons low-sodium soy sauce, sesame oil, optional sake, and black pepper. Stir in one direction for 1–2 minutes until the mixture looks cohesive and slightly sticky. Refrigerate while setting up the folding area. Do not taste the raw pork mixture. Keep it cold until assembly.
Fill the wrappers. Lay one gyoza wrapper flat and place a dried shiso leaf in the center, folding the leaf slightly if it is too large. Add about 1 level tablespoon of filling over the leaf, using less if the wrapper is small. Moisten the wrapper's outer edge lightly with water. Repeat with the remaining wrappers and filling. A little room around the filling makes sealing much easier.
Shape and seal. Fold each wrapper into a half-moon, pressing or pleating the edges tightly to close. Set the finished dumplings on a lightly dusted tray, flat side down, and keep them covered while you shape the rest. You should have 16 dumplings. Press out trapped air without squeezing filling through the seam.
Pan-fry and steam in batches. Heat 1 tablespoon neutral oil in a large nonstick skillet over medium heat. Arrange 8 dumplings in a single layer, flat sides down, and fry for about 2 minutes until the bases begin to turn golden. Carefully add 1/4 cup (60 ml) water and immediately cover with a lid. Steam for roughly 5–6 minutes, then uncover and let the water evaporate, cooking about 1 minute more to re-crisp the bases. Check that the center of the pork filling reaches at least 160°F (71°C); continue cooking covered with a splash of water if necessary. Repeat with the remaining dumplings, oil, and water. Use a food thermometer; exact cooking time varies with wrapper thickness, filling size, and skillet temperature.
Mix the dipping sauce. Stir 1 tablespoon low-sodium soy sauce and 1 tablespoon rice vinegar together in a small serving bowl. Add chili oil if desired. Offer the sauce separately so the gyoza bottoms stay crisp.
Serve hot. Transfer the dumplings to plates with the browned sides facing upward. Serve four gyoza per person with the dipping sauce. Refrigerate any leftovers promptly. The contrast between a golden base and tender upper wrapper is best just after cooking.
