For the dumplings: In a large bowl, combine the beef, scallions, mushrooms, garlic, ginger, soy sauce, corn starch, and mix well.
Lay down the dumpling wrappers on a dry, clean surface, brush lightly with water, and place a teaspoon of filling in the center. Fold one point of the wrapper over the filling to the opposite point of the wrapper, and press tightly along the edges to seal them shut. Set aside on a piece of plastic wrap or dry surface.
Heat a large sauté pan 1/2 of the way filled with water to a low simmer. Then turn down the heat so there is no movement in the water.
Place the dumplings in a single layer in the water (in batches if needed, not to overcrowd the pan) and cover with a lid. Steam for approximately 6 minutes. Remove with a slotted spoon onto a paper towel to drain any excess water.
For the sauce: In a saucepan over low-medium heat, whisk together all ingredients until the sauce is thick and smooth.
Toss the dumplings in the sauce and serve. Garnish with scallions.