In a large bowl, combine the filling ingredients. Mix thoroughly with a spoon or your hands until the mixture becomes sticky and cohesive.
In a small bowl, whisk together the sauce ingredients. Put it over low heat while you cook the dumplings, just to let the sugar dissolve.
Heat the neutral oil in a large nonstick skillet over medium heat. Scoop about 1 1/2 tablespoons of the pork filling and place it directly into the skillet, forming a small mound. Repeat with the remaining filling, leaving a little space between each one.
Place one potsticker wrapper over each mound of filling, gently draping it over the top like a blanket. Lightly press the wrapper around the filling so it settles into place. If the wrappers feel dry, brush or dab them lightly with water.
Carefully pour 1/2 cup water into the skillet. Cover with a lid and steam for 6–8 minutes, or until the filling is cooked through and the wrappers are tender.
Remove the lid and let any remaining water evaporate. Continue cooking for 1–3 minutes, or until the bottoms are golden brown and crispy.
Transfer the blanket dumplings to a serving plate and serve warm with the soy-ginger sesame dipping sauce and green onions.