Set aside about 2 oz (a loose handful) of noodles for frying. Heat the 1 cup of oil in a wok or small pot over medium-high heat. Fry the reserved noodles in small batches for 30 to 60 seconds, until puffed, golden, and crisp. Drain on paper towels. They burn fast, so pull them a shade early.
Boil the remaining noodles until just tender with a little chew left, 2 to 4 minutes for fresh or according to the package for dried. Drain, rinse briefly, and toss with a teaspoon of the frying oil so the strands do not glue together.
Keep 2 tablespoons of the frying oil in the pot (or use fresh oil in a Dutch oven) over medium heat. Add the curry paste, ginger, turmeric, coriander, and cumin. Fry, stirring constantly, for 2 to 3 minutes, until the paste darkens and smells deeply fragrant.
Pour in the coconut milk and stir until smooth. Simmer gently 3 to 4 minutes, until beads of orange oil show at the edges. Add the stock and bring back to a bare simmer.
Add the chicken and simmer 15 to 20 minutes, until tender and cooked through. Keep the broth at a lazy simmer; do not let it reach a rolling boil.
Stir in the fish sauce, palm sugar, and soy sauce. Taste and adjust: savory first, then warm and rich, with the sugar only rounding the edges. Add salt or more fish sauce if flat.
Divide the boiled noodles among four warm bowls. Ladle the broth and chicken over the top. Finish each bowl with a mound of crispy noodles, pickled mustard greens, shallot, and cilantro. Serve with lime wedges and chili oil.