In bowl combine 1/2 cup coconut milk, fish sauce, 2 teaspoons red curry paste, 1 teaspoon brown sugar, ciclantro, and turmeric.
Slice the chicken into long, thin strips, about 3 inches long by 1 inch wide, and add to marinade. Turn chicken to coat. cover and refrigerate for up to 4 hours.
While marinating, bring the 1 cup coconut milk to a simmer. Whisk in 2 tablespoons curry paste until dissolved. Whisk in peanut butter, stock and 1/4 cup brown sugar, reduce heat and cook until smooth, stirring constantly, about 5 minutes. Remove from heat and ad lime juice. Set aside to cool to room temperature.
Prepare relish: Peel, half, and thinly slice cucumber. Thinly slice shallots and chili. Mix in a small bowl. Heat the vinegar, 3 teaspoons brown sugar, and 1 teaspoon salt in a small saucepan, stirring until mixture reaches a boil and sugar is dissolved, about 3 minutes. Remove from heat, cool to room temperature, and then pour over cucumber mixture.
Prepare grill and thread marinated chicken onto soaked bamboo skewers. Place on grill and cook 5 to 7 minutes, or until cooked through, turning once. Serve with peanut butter sauce and cucumber relish.