Heat the oil in a large pot over medium heat. When it shimmers, add the garlic, ginger, and Thai red curry paste and cook, stirring constantly, until dark red and very fragrant, about 5 minutes. Add the chicken broth, coconut milk, fish sauce, lemongrass, 1 teaspoon salt and a pinch of sugar. Bring the mixture to a boil, then reduce the heat to a simmer and cook, uncovered, until the lemongrass and ginger are tender, about 15 minutes. Discard the lemongrass.
Meanwhile, put the noodles in a medium bowl and cover with hot water. Let stand for 10 minutes, then drain and set aside. Toss together the red onion, cilantro, scallions and Thai basil in a medium bowl and set aside.
Stir the chicken into the broth and simmer over low heat until tender, 5 minutes for chicken breast and about 15 minutes for chicken thighs. Increase the heat to high and stir in the noodles. Bring the soup to a boil, then immediately remove from the heat. Stir in the lime juice. Serve the soup in bowls topped with the reserved onion and herb mixture.
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