How to Make It
In a heatproof bowl, soak the árbol chiles in the boiling water until softened, about 10 minutes. Drain the chiles. In the bowl of a food processor, combine the árbol chiles with the Thai chiles, lemongrass, shallots and garlic and puree until smooth.
In a medium bowl, toss the chicken with the turmeric, cinnamon and 1 tablespoon of kosher salt. In a large, deep skillet, heat the oil until shimmering. Add half of the chicken thighs and cook over moderately high heat, turning once, until browned on both sides, about 8 minutes total; transfer to a plate. Repeat with the remaining chicken.
Add the chile puree to the skillet and cook over moderate heat, stirring, until golden brown, about 5 minutes. Add the ketchup, vinegar, sugar and 1/2 cup of water and bring to a simmer. Return the chicken to the skillet and simmer over moderately low heat until the chicken is tender and cooked through, about 15 minutes.
Meanwhile, in a medium pot of salted boiling water, cook the carrots until crisp-tender, about 3 minutes; drain. Add the carrots and peas to the chicken and simmer until heated through, about 5 minutes. Stir in the mint and season with salt. Transfer the chicken to a platter and spoon the sauce over the top.
The cooked chicken can be refrigerated in the sauce overnight.