Heat 2 tablespoons vegetable oil at the bottom of a soup pot over medium-high to high heat, add shrimp, chicken or pork and stir-fry -- shrimp until just pink, chicken or pork until lightly browned. Add mushrooms, carrots and garlic; cook 2 minutes. Add cabbage and cook until wilted, about 5 minutes.
While the cabbage cooks, add 2 tablespoons vegetable oil to a skillet and arrange pot stickers in it. Add 2/3 cup water and turn heat to medium-high. Cook 8 minutes to evaporate the water then let the pot stickers brown on the bottom, about 1 minute more.
Add scallions, tamari and some black pepper to the soup pot, stir to combine, then add stock and bring to a boil. Pour in beaten eggs and stir the pot until the eggs are cooked and scattered throughout the stoup.
Place a few potstickers in the bottom of a soup bowl and top with Moo Shu Stoup. Yum-O!