Make the chicken. In a small bowl combine coconut milk, garlic, turmeric, cilantro, brown sugar, fish sauce, and salt.
Pat the chicken dry. Using a mallet or rolling pin, pound the chicken tenders until very thin. Arrange the chicken in a single layer in a baking dish or rimmed baking sheet, then pour the marinade over top. Cover and marinate, refrigerated for 2 hours or up to overnight.
Meanwhile, make the peanut sauce. In a small saucepan, add the coconut milk, curry paste, peanut butter, salt, sugar, vinegar, and ½ cup water; whisk to combine. Bring the sauce to a simmer over low heat and cook, whisking, until slightly thickened, about 5 minutes. Remove the saucepan from heat and let sit for 10 minutes before serving. If the sauce gets too thick while cooling, reheat it over low and add a splash or two of water.
Preheat the grill on medium. Tightly thread the chicken onto the skewers, dividing evenly. Place the skewers on the grill and cook, undisturbed, 3-5 minutes per side. Transfer to a serving platter.
Garnish the chicken with cilantro and peanuts. Serve with the peanut sauce on the side.