Place the dried sotanghon in a bowl and cover with warm water. Soak until flexible but still slightly firm. Drain very thoroughly, then cut the noodles into shorter, easy-to-wrap lengths.
Heat 1 tablespoon neutral oil in a large skillet over medium-high heat. Add the garlic and onion and cook, stirring, until fragrant and the onion begins to soften. Add the carrots and green beans and cook for about 2 minutes.
Add the cabbage and bean sprouts. Cook while tossing until the cabbage begins to wilt but the vegetables still retain some structure. There should be no pool of liquid at the bottom of the pan.
Add the drained noodles, soy sauce, sesame oil, black pepper, and green onions. Toss until the noodles absorb the seasoning and are tender but still separate. Cook off any visible excess moisture, then remove from the heat.
Spread the filling in a relatively thin layer on a sheet pan or large plate. Let it cool until no longer warm. Do not wrap hot filling.
Place one wrapper in a diamond position. Add about 1/3 cup filling across the lower third, leaving space around the edges. Fold the bottom corner over the filling, fold both side corners inward, and roll firmly without tearing. Moisten the final corner lightly with water and seal. Repeat to make 12 rolls.
Heat about 1 to 1 1/2 inches neutral oil to 350°F.
Working in batches so the pan is not crowded, carefully lower the lumpia into the oil. Fry, turning as needed, until evenly deep golden, crisp, and firm rather than leathery, about 3 to 4 minutes per batch. Transfer to a wire rack and do not stack while hot.
Let the rolls stand for a few minutes so the filling is not dangerously hot, then serve while crisp with your preferred dipping sauce.