How to Make It
In a food processor, combine the fresh and dried red chiles, lemongrass, garlic, coarsely chopped shallots and water and process to a fine paste.
In a large, deep skillet, heat 3 tablespoons of the vegetable oil. Season the chicken with salt and cook over moderately high heat, turning once, until browned on both sides, about 10 minutes. Transfer the chicken to a plate.
Reduce the heat to moderate and add the chile paste. Cook, stirring constantly, until the paste begins to stick to the bottom of the pan and brown, about 7 minutes. Stir in the coconut milk and return the chicken to the skillet. Cover partially and simmer over moderately low heat until the chicken is cooked through and the sauce has thickened, about 25 minutes.
Meanwhile, in a medium skillet, heat the remaining 6 tablespoons of vegetable oil. Add the thinly sliced shallots and fry over moderate heat, stirring occasionally, until golden brown, about 10 minutes. Using a slotted spoon, transfer the shallots to paper towels to drain.
Transfer the chicken to plates. Add the lemon juice to the sauce and season with salt and pepper. Spoon the sauce over the chicken and sprinkle with the shallots.