Heat oil in a 14 inch flat-bottomed wok or very large frying pan over medium-high heat. Add pork and cook, stirring until browned, 8–10 minutes.
Add garlic, ginger, and chile paste. Cook, stirring, until fragrant, about 1 minute.
Add sugar, soy, and vinegar. Cook, stirring, until sugar dissolves.
Add 6 cups water and bring to a boil. Reduce heat to medium and cook until pork is very tender, about 2 hours.
Return to boil, add cornstarch mixture, and cook, stirring, until slightly thickened, 1–2 minutes. Keep soup warm.
Bring a large pot of salted water to a boil and cook noodles until tender, 3–5 minutes. Drain and divide between 6 large serving bowls. Ladle soup over noodles and garnish with scallions and pickled chiles.