In a medium saucepan, whisk together coconut milk and peanut butter until nearly smooth. Whisk in broth, soy sauce, vinegar, brown sugar, sesame oil, curry paste, ginger, garlic, and cayenne pepper. Bring just to boiling over medium-high heat; reduce heat. Simmer, uncovered, for 15 minutes, stirring occasionally.
Preheat oven to 300 degrees F. In a plastic bag, combine flour, salt, and black pepper. If desired, remove skin from chicken. Add chicken pieces, one at a time, to flour mixture, shaking to coat.
In a large skillet, cook chicken, half at a time, in hot oil until brown, turning occasionally. Transfer chicken to an ungreased 3-quart rectangular baking dish. Pour peanut butter mixture over chicken. Cover loosely with foil. Bake for 1 hour for chicken (1-1/2 hours for Cornish hens), occasionally spooning sauce over chicken. Bake, uncovered, for 20 to 30 minutes more or until chicken is very tender.
Transfer chicken to a serving platter. Skim fat from sauce in dish. Spoon some of the sauce over chicken. Sprinkle with cilantro. Serve with the remaining sauce and hot cooked rice. Makes 4 servings.