Place a large skillet over medium-high heat. Add the sesame oil, ground pork, grated ginger, and garlic.
Brown the ground pork and break it into small pieces with a wooden spoon. Once the pork is mostly cooked through, stir in the shredded cabbage, carrots, and soy sauce. Cook until the cabbage has softened, about 5 minutes. Taste, then salt and pepper as needed.
Meanwhile set a 8- to 9-inch nonstick skillet over medium heat. Crack the eggs into a measuring pitcher, until you have 2 cups worth. Add the salt and whisk until frothy.
Add 1 teaspoon of oil or butter to the skillet. Use a 1/3-cup scoop to portion the egg mixture into the skillet. Swirl it around the skillet into an even layer and cook 1-2 minutes. Once set, carefully flip the egg wrap and cook another 30-60 seconds. Then move it to a cutting board. Repeat five more times with the remaining butter/oil and eggs.
Lay each egg wrap out and scoop 1/6 of the pork filling on one half of each wrap. Fold the edge of the egg wrap over the filling and fold the sides inward, like a burrito. Roll the egg wrap, tucking in the edges to fully enclose the filling. Serve as-is, or cut in half. Serve warm or at room temperature.
These actually make great leftovers and lunchbox items!