In a large pot, place pork face and pig brains in a heat-safe resealable plastic and pour about 6 cups of water. Add onions, garlic, peppercorns, salt, and 1/2 cup soy sauce then bring to a boil. Simmer until soft for about 1 hour. Once soft, take out the pork and pat dry with a towel.
Grill or place in the oven until crispy. Set aside to cool. Once cool, mince the cooked pork and set it aside.
In a pan, sauté the onions in oil over medium heat for a few minutes, until aromatic.
Add the minced pork and mix until well combined. Adjust taste with garlic, pepper, soy sauce, and calamansi if necessary. Set aside.
On a clean surface, place about 1/2 a tablespoon of filling in the middle of a dumpling wrapper.
Fold into a half-circle and fold the edges, brushing with cornstarch mixed with water to seal.
In a pan with a bit of oil, place gyozas and heat until the bottom of the gyozas is brown.
Fill the pan with water until the bottom of the gyozas is covered. Cover the pan and allow to steam until cooked. Set aside.
Mix all ingredients in a bowl.
Serve with the cooked gyoza.
Servings 0