Pork Gyoza with Ginger Dipping Sauce

Name: Pork Gyoza with Ginger Dipping Sauce
Ingredients: 1/4 cup low-sodium soy sauce; 2 tablespoons rice vinegar; 1 teaspoon toasted sesame oil; 1 teaspoon sugar; 1/2-inch piece fresh ginger, peeled and cut into thin strips; 8 ounces ground pork; 1 large egg; 1 tablespoon toasted sesame oil; 1 tablespoon finely chopped ginger; 2 teaspoons grated garlic (from about 3 large cloves); 1 scallion, thinly sliced; 1 1/2 teaspoons low-sodium soy sauce; 1 1/2 teaspoons dry vermouth; 1 teaspoon cornstarch; 1/2 teaspoon sugar; Kosher salt; 34 gyoza wrappers or round dumpling wrappers; 4 tablespoons vegetable oil