Heat 2 tablespoons oil in a wok or large skillet over medium heat; cook and stir chopped shallots and garlic until garlic starts to turn golden, 2 to 4 minutes. Add red curry paste and curry powder; cook and stir until fragrant, 1 to 2 minutes. Add coconut milk, water, chicken, and sea salt; bring to a boil. Reduce heat to medium low and simmer soup.

Mix fish sauce, sugar, and lime juice into soup and simmer until heated through, about 10 minutes more.

Heat 1/2 cup oil in a skillet over medium-high heat; fry Thai chile peppers until browned, 2 to 4 minutes. Transfer chile peppers to soup, reserving oil in skillet. Fry quartered shallots and bok choy in hot oil until browned, 2 to 4 minutes; transfer to soup and reserve oil in skillet.

Place noodles in a large bowl and cover with hot water. Set aside until noodles are softened, about 15 minutes. Drain and rinse thoroughly. Add 3/4 of the noodles to the soup. Fry the remaining rice noodles in the hot oil until crisp, 3 to 5 minutes.

Divide soup among 6 bowls and top with fried noodles, pickled cabbage, cilantro, and lime wedges.