Finely mince the shrimp and place in a medium mixing bowl with the ground pork and shredded green cabbage.
Add the grated ginger, minced garlic, toasted sesame oil, sea salt, and black pepper to the meat mixture and mix until well combined.
Lay the dumpling wrappers on a clean surface and place a rounded tablespoon of the filling in the center of each.
Lightly moisten the edges of the wrappers with water, fold them in half over the filling, and pinch the edges to create small pleats, ensuring they are tightly sealed.
Heat the avocado oil in a large non-stick skillet over medium-high heat.
Place the dumplings in the skillet and sear for 2 to 3 minutes until the bottoms are golden brown and crispy.
Carefully pour the water into the pan and immediately cover with a tight-fitting lid to steam the dumplings for 5 minutes.
Remove the lid and continue to cook for another 1 to 2 minutes until the remaining water has evaporated and the bottoms have re-crisped.
Serve the dumplings hot, garnished with sliced green onions and tamari on the side for dipping.