Stir cornstarch and water in a small bowl to make a smooth sealing slurry; set aside.
Heat 1 tbsp oil in a large skillet over medium-high heat.
Cook the pork, breaking it up, until browned and no longer pink, 4-5 minutes. Drain excess fat if needed.
Add garlic and ginger; sauté until fragrant, about 30 seconds.
Stir in cabbage and carrot; cook until slightly wilted, 3-4 minutes.
Season with soy sauce, sesame oil, rice vinegar, pepper, and a pinch of salt. Fold in green onions and let the filling cool 10 minutes.
Place a wrapper on the counter like a diamond. Spoon 2-3 tbsp filling near the bottom corner.
Fold bottom corner over filling, tuck in sides, then roll up tightly. Brush edge with slurry to seal. Repeat with remaining wrappers.
Heat 4 cups oil in a deep pot to 350°F. Fry rolls in batches until golden and crisp, 3-4 minutes, turning once.
Drain on a rack or paper towels. Serve hot with your favorite dipping sauce.