Mix the filling. Combine the pork, cabbage, carrots, onion, garlic, soy sauce, salt, pepper, and beaten egg in a large bowl. Mix with clean hands just until evenly distributed, about 1 minute; stop as soon as you no longer see streaks of plain pork.
Chill for easy rolling. Cover and refrigerate the filling 20 to 30 minutes so it firms up and portions neatly without weeping moisture into the wrappers.
Set up your rolling station. Peel the wrappers apart and keep them under a barely damp towel. Lay one wrapper in a diamond shape, one corner pointing at you, with the filling, a tablespoon, and the cornstarch paste within reach.
Fill and fold. Spoon about 1 1/2 tablespoons of filling in a horizontal line across the lower third of the wrapper, leaving about 1 inch at each side. Fold the bottom corner up over the filling, fold both side corners in, then roll upward snugly with no air pockets.
Seal the edge. Brush the top corner with a thin line of cornstarch paste and finish the roll. Rest completed rolls seam side down on a tray under a damp towel.
Heat the oil to 350°F (175°C), about 1 1/2 inches deep in a heavy pot or deep skillet. A scrap of wrapper should sizzle on contact and turn golden in about 30 seconds.
Fry in batches of 6 to 8, seam side down first, without crowding. Fry 3 to 4 minutes, turning occasionally, until deeply golden on all sides; judge the last minute by color.
Drain upright on a wire rack over a tray for the first minute so oil escapes from the seam. Do not use paper towels, which trap steam and soften the crust.
Serve right away with banana ketchup, sweet chili sauce, or garlic vinegar for dipping.