Combine water, salt, and cornstarch in a measuring cup or bowl and mix. Set aside.
Heat oil in frying pan. Add the dumplings and arrange in a flower pattern. Do not over-crowd the pan, as this will make it difficult to flip onto the plate. You can fit 10-12, but add less dumplings if you want more of the crispy skirt. Cook 2-3 minutes or until you hear a distinct sizzling sound.
Mix the cornstarch slurry once more, as cornstarch tends to settle to the bottom. Pour in the mixture. For fresh dumplings, add enough to cover ¼ of the way up. For frozen, have the liquid cover ⅓ of the dumplings to allow for more cook time.
Steam dumplings covered for 5-6 minutes. First, you will hear a boiling sound as the water from the slurry begins to evaporate. As it changes, listen for the frying sound to uncover the pan. The dumpling skirt will have formed and the edges will release from the pan.
To transfer dumplings to a plate, hold plate face-down on top the dumplings with one hand. Then invert frying pan upside-down turning plate right-side up at the same time. Garnish with green onions.
To make the dumpling sauce, first dissolve sugar in hot water. Then stir in the remaining ingredients.