1. Preheat oven to 375°.
2. To prepare the chicken, place first 7 ingredients in a food processor, and process until finely minced.
3. Discard giblets and neck from chicken. Pat dry. Trim excess fat. Starting at neck cavity, loosen skin from breast and drumsticks by inserting fingers, gently pushing between skin and meat. Spread cilantro mixture under loosened skin. Lift wing tips up and over back, and tuck under chicken.
4. Place chicken, breast side up, on a broiler pan coated with cooking spray. Bake at 375° for 1 1/4 hours or until an instant-read thermometer inserted into the thickest part of the thigh registers 165°. Cover chicken loosely with foil; let stand 10 minutes. Discard skin.
5. To prepare rice, combine rice, 1 cup water, 1/2 teaspoon salt, sliced ginger, cinnamon stick, and coconut milk in a medium saucepan; bring to a boil. Cover, reduce heat, and simmer 15 minutes or until liquid is absorbed and rice is tender. Let stand, covered, 5 minutes. Fluff with a fork. Remove and discard ginger slices and cinnamon stick. Serve with chicken.