Marinate Chicken: In a zip-top plastic bag, combine 1/4 cup coconut milk, 1 Tablespoon red curry paste, ground turmeric, 1 teaspoon sugar, and 1 teaspoon salt. Add chicken and seal bag. Squeeze bag gently to press marinade into chicken. Marinate chicken for at least 10 minutes and up to a day (if it will be more than 10 minutes, refrigerate chicken while it marinates).
If using wooden / bamboo skewers, soak them in water for 10 minutes to minimize burning.
Make Peanut Sauce: Combine 1 1/4 cups coconut milk and 2 Tablespoons red curry paste in a small saucepan over low-medium heat, whisking constantly as it begins to warm up. When the mixture begins to bubble, reduce heat to a low simmer (don't let it boil vigorously). Whisk in peanut butter, sugar, and fish sauce. Continue to simmer, whisking frequently, until thick, 4 to 5 minutes more. Move off the heat to cool slightly.
Heat Grill or Broiler: If cooking on a grill, heat grill. If using the oven, turn on the oven’s broiler.
Spray a rimmed sheet pan with nonstick cooking spray (you can also line it with foil first to make clean-up even easier).
Working with one at a time, thread chicken onto skewers. Place the skewers in a single layer on the sheet pan with the end of each skewer propped up on the rims of the pan so that the chicken sits slightly above the pan. (Discard any leftover marinade.)
Cook Satay: Grill satay until golden on the outside and cooked through. Or, if using the broiler, slide the pan under the broiler and cook, flipping halfway through cooking, until chicken is browned on both sides and cooked through, 5 to 10 minutes total. (Important: If using the broiler, turn on your oven fan before cooking and keep a close eye on the satay. Broiling the satay can cause some splatter / smoking.)
Serve satay over rice with peanut sauce for dipping and any optional garnishes. Enjoy!