In a large pot of boiling salted water, cook the spinach and snow peas just until the spinach wilts, 30 seconds. Remove the vegetables. Add the noodles to the water and cook until al dente, 8 minutes. Drain well. Transfer the spinach, snow peas and noodles to bowls.
Meanwhile, in a large saucepan, heat 1 tablespoon of the oil. Cook the shallots over moderately high heat until lightly browned, 2 minutes; transfer to a plate. Reduce the heat to moderate. Add the remaining 2 tablespoons of oil, the garlic, curry paste, curry powder, coriander and turmeric and stir-fry for 30 seconds. Add the stock, bring to a boil and cook for 3 minutes. Add the coconut milk, fish sauce and sugar, bring to a boil and cook for 5 minutes. Add the chicken, cilantro and scallions and cook just until heated through; season with salt. Ladle the soup over the noodles and serve with the cooked shallots, lime wedges and sliced chiles.