Make the sauce: Combine all ingredients in a medium bowl. Set aside to serve alongside the dumplings. 

Heat 2 tablespoons of the sesame oil in a large skillet over medium-high heat. When the oil shimmers, add the shallots and cook until fragrant and lightly caramelized for about 2 minutes. Add the mushrooms, ginger, and garlic. Cook, stirring occasionally, until the mushrooms have cooked down for about 5 minutes. Add the soy sauce and freshly ground black pepper. Stir in the greens and cook for another 2 to 3 minutes, until the mushrooms are caramelized. Remove from the heat and let cool.

To assemble, spoon 1 tablespoon of filling onto each wrapper. Brush water around the edges of the wrapper. Fold the edges of the wrapper up around the filling and pinch in the center to seal. Repeat with the remaining wrappers.

Place the sesame seeds in a shallow bowl. Brush the bottoms of the dumplings with water, then dredge them in the sesame seeds.

Heat the remaining 2 tablespoons of sesame oil in a large skillet set over medium heat. When the oil shimmers, add the dumplings with the sesame seed side down and cook until the bottoms are light golden brown, for about 2 to 3 minutes. Carefully pour 1/4 cup of water into the skillet. Stand back since it will splatter. Immediately cover with a tight-fitting lid. Turn heat to medium-low and let the dumplings steam for about 5 minutes.

Garnish with the green onion slices and serve while still warm with the dipping sauce.

To Freeze: Fill and form the dumplings. Dredge the bottoms in sesame seeds then flash-freeze the dumplings on a baking sheet for 30 minutes. Transfer the dumplings to a freezer bag and freeze for up to 3 months. When ready to enjoy, thaw overnight in the refrigerator, then proceed as directed to pan fry and steam.