Place vegetable oil, soy sauce, tamarind paste, lemon grass, garlic, cumin, coriander, lime juice, muscovado sugar, and chili powder in a blender and process to a smooth paste. In a large bowl, or a large resealable plastic bag, toss chicken strips with marinade. Refrigerate for 1 hour.
Preheat an outdoor grill for medium-high heat, and lightly oil the grate.
In a small saucepan, combine peanut butter, peanuts, coconut milk, curry paste, fish sauce, tomato paste, and brown sugar. Cook and stir over medium-low heat until smooth. Keep warm.
Thread chicken onto skewers. Grill until no longer pink in the center, 3 to 5 minutes on each side. Serve with peanut sauce.
