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