To make the shumai, line a few of the green dumpling wrappers on a clean, smooth surface. Pipe a quarter-size amount of filling in the middle of each wrapper. Carefully gather the surrounding edge of the dumpling wrapper around the filling and pinch until the filling is completely enclosed in the wrapper. Repeat with the remaining wrappers and filling. Store the shumai in the refrigerator until ready to cook.
For the topping: Cook the shallots, garlic and chile flakes in the olive oil until soft and translucent. Lightly mash the peeled tomatoes with a whisk in a large container until broken up but still chunky. Add to the shallot mixture. Season with salt and sugar. Turn up the heat and bring to a boil, then reduce the heat to a low simmer and continue to cook until almost all of the water is cooked out. The resulting product should be very concentrated. Taste and adjust the seasoning. Remove from the heat and stir in the pickled ginger. Cool in refrigerator until ready to use.
For cooking the shumai: Spray a steamer basket with nonstick spray and place it over an appropriate-size pot approximately one-third full of water. The base of the basket should rest above the surface of the water. Bring the water to a boil, and then lower to a simmer. Top each shumai with a small amount of the tomato mixture and place a few in the steamer basket at a time, ensuring that the edges are not touching each other. Cover and steam until cooked through, about 8 minutes.