Heat 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, 2 minutes. Add the mushrooms, ginger, and garlic, and cook, stirring occasionally until the mushrooms have cooked down, about 5 minutes. Add the soy sauce and large pinch of pepper. Stir in the greens. Cook another 2-3 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 and then dredge them in the sesame seeds.Heat a few tablespoons of oil in a large skillet set over medium heat. When the oil shimmers, add the dumplings and cook until the bottoms are light golden brown, about 2-3 minutes. Carefully pour 1/4 cup of water into the skillet, it will splatter, so stand back. Immediately cover with a tight-fitting lid. Turn heat to medium-low and let the dumplings steam for 5-6 minutes. Serve warm with sauce (see below) and green onions. To make the sauce, combine all ingredients in a medium bowl. Serve alongside the dumplings.