Prepare the Broth: In a large pot, combine chicken broth, water, rehydrated shiitake mushrooms (sliced), reserved mushroom soaking liquid (strain it first!), ginger, garlic, and white parts of green onions. Bring to a boil, then reduce heat and simmer for at least 30 minutes, or up to an hour, to allow the flavors to meld.

Prepare the Gyoza Filling: In a large bowl, combine ground pork, napa cabbage, green onions, soy sauce, rice vinegar, sesame oil, ginger, garlic, and white pepper. Mix thoroughly until well combined.

Assemble the Gyoza: Place a gyoza wrapper in the palm of your hand. Add about 1 teaspoon of filling to the center of the wrapper. Dip your finger into the bowl of water and moisten the edges of the wrapper. Fold the wrapper in half to form a half-moon shape. Pleat one side of the wrapper, pressing firmly to seal. Repeat until all the filling is used.

Cook the Gyoza: You have two options:

Option 1 (Pan-Fried and Steamed): Heat 1 tablespoon of oil in a large non-stick skillet over medium heat. Arrange the gyoza in the skillet, flat side down, without overcrowding. Cook for 2-3 minutes, or until the bottoms are golden brown. Add 1/2 cup of water to the skillet, cover, and steam for 5-7 minutes, or until the water has evaporated and the gyoza are cooked through.

Option 2 (Boiled): Bring a large pot of water to a boil. Gently drop the gyoza into the boiling water. Cook for 3-4 minutes, or until they float to the surface and are cooked through.

Strain the Broth: Strain the broth through a fine-mesh sieve to remove the solids. Discard the solids.

Finish the Soup: Return the strained broth to the pot. Add soy sauce, mirin, and sesame oil. Bring to a simmer.

Serve: Divide the cooked gyoza among bowls. Ladle the hot broth over the gyoza. Garnish with green onions, toasted sesame seeds, chili oil (if using), and fresh cilantro (if using).