In a large bowl combine the beef, mushrooms, garlic, and minced scallions. Mix well.
Lay one wonton wrapper on a dry, clean surface and place approximately a good sized teaspoon of filling in the center. Dip your finger in a cup of water and run it along the edges of the dumpling wrapper. Gently fold one tip the wonton to the opposite side creating a triangle and gently press along the edges to crimp them tight and seal them shut so there are no openings. Repeat with the remaining wrappers. Set them aside on a plate or sheet pan for to dry for 5 - 10 minutes.
Bring a large saute pan 1/4 of the way filled with water to a simmer. Place the dumplings in a single layer in the pan (in batches if needed, not to overcrowd the pan) and cover with a lid. Steam for approximately 6 - 8 minutes or until the internal temperature reaches 155 degrees using a thermometer. Remove with a slotted spoon onto a paper towel to drain any excess water. (don't poke holes in all of them with the thermometer to check the temperature, just check one)
For the sauce: In a bowl dissolve the cornstarch in water completely. In a sauce pan on medium heat bring the soy sauce to a simmer, whisk in the cornstarch and stir until it thickens to a smooth consistency. Remove from heat and set aside.
Heat the oil in a nonstick pan on medium high heat. Saute the snow peas for 2 - 3 minutes until they are somewhat soft but still hold a crunch.
Lay the snow peas down, place the dumplings on top, and the pickled ginger on the side. Drizzle the soy glaze over top and serve.