In a medium bowl, stir together the chicken, garlic, ginger, turmeric, paprika, cayenne, 1½ teaspoons salt and 1 tablespoon of the fish sauce. In a small bowl, whisk together the chickpea flour and 1 cup of the broth; set aside.
In a large Dutch oven over medium, heat the oil until shimmering. Add the onions and ½ teaspoon salt. Cook, stirring occasionally, until light golden brown, 12 to 15 minutes; reduce the heat if the onions are browning too quickly. Add the chicken and cook over medium, stirring occasionally, until opaque on the exterior, about 5 minutes.
Stir in the remaining 3 cups broth, the remaining 3 tablespoons fish sauce, the coconut milk and 3 cups water. Bring to a simmer over medium-high. Whisk the chickpea flour mixture to recombine, then whisk it into the broth mixture. Return to a simmer and cook, uncovered and stirring occasionally, until the chicken is cooked through, about 15 minutes. Off heat, taste and season with salt.
While the soup simmers, bring a large pot of water to a boil. Add the noodles and cook, stirring occasionally, until tender. Drain in a colander and rinse under cold water, shaking the colander to remove as much water as possible. Divide the noodles evenly among 4 serving bowls, then ladle the soup over the noodles. Serve with lime wedges.
