Finely mince the garlic, ginger, onion, water chestnuts, and shrimp so they are uniform in size.

In a large mixing bowl, combine ground pork, chopped shrimp, minced onion, garlic, ginger, soy sauce, sesame oil, egg white, salt, and white pepper; mix gently until just combined.

Pinch off a small piece of the filling and cook it in a pan for 10 seconds to taste and adjust seasoning as needed.

Place wonton wrappers on a cutting board and keep them covered with a damp towel to prevent drying.

Place 1 teaspoon of filling in the center of each wonton wrapper and moisten the edges with water.

Fold the wrapper into a triangle, seal the edges, then bring the two side corners together and press to form a nurse's cap shape.

Repeat the wrapping process with the remaining filling and wrappers, arranging each siomai on a plate without touching.

Heat a large non-stick skillet over medium-high heat and add 2 tablespoons vegetable oil, swirling to coat the pan.

Place siomai flat-side down in the hot skillet and cook undisturbed for 2 to 3 minutes until the bottoms are golden brown.

Pour 1/4 cup water into the skillet and immediately cover with a lid; reduce heat to medium and steam for 5 to 7 minutes until filling is cooked through.

Remove the lid, let any remaining liquid evaporate for 1 to 2 minutes to crisp the tops, then transfer siomai to a plate lined with paper towels.

In a small bowl, whisk together vinegar, soy sauce, minced garlic, and sliced chili to make the dipping sauce; adjust flavors to taste.

Serve the siomai hot with the dipping sauce alongside for dunking.