Cook the ground pork in a large skillet over medium-high heat, breaking it into small crumbles, until fully browned and no pink remains, about 6 to 7 minutes. Drain any excess fat.
Add the cabbage, carrots, garlic, and ginger to the skillet. Cook for 3 to 4 minutes, stirring frequently, until the vegetables soften slightly but still have some crunch. Stir in the tamari, sesame oil, white pepper, and green onions. Remove from heat and let the filling cool for about 10 minutes so it is easy to handle.
Fill a large shallow dish with warm water. Working one at a time, dip a rice paper wrapper into the water for about 5 to 8 seconds until it just begins to soften but is still slightly firm. Lay it flat on a clean, damp surface.
Place about 3 tablespoons of filling in the lower third of the wrapper. Fold the bottom edge up over the filling, fold in both sides tightly, then roll up firmly like a burrito. The wrapper will stick to itself as it softens. Repeat with the remaining wrappers and filling.
Heat about 2 inches of vegetable oil in a large heavy-bottomed pot to 350 degrees F. Fry the egg rolls in batches of 3 to 4 for about 3 to 4 minutes, turning occasionally, until deeply golden and shatteringly crispy all over. Transfer to a wire rack.
Let them rest for 2 minutes so the exterior firms up even more. Serve hot with gluten free sweet and sour sauce for dipping.