Season the chicken pieces with salt and cayenne pepper.
Heat the oil in a large dutch oven over medium high heat and sear chicken pieces on both sides until golden brown. Remove to a platter and reserve.
Add butter to pan and when melted, add flour, and stir to combine well. Continue to cook roux, stirring constantly, until chocolate brown, about 12 to 15 minutes.
Immediately add onion, celery, bell pepper, and bay leaves and cook until soft, 2 to 3 minutes. Add garlic and cook another 2 minutes, then add the beer and stir well to loosen any brown bits from pan bottom. Add the stock, brown sugar, hot sauce, and Worcestershire sauce and stir to combine well. Bring to a boil, return chicken pieces to the pot, and simmer for 1 hour and 15 minutes, until chicken is very tender.
Remove chicken pieces to a platter and when cool enough to handle, remove chicken meat from the bones. Return chicken meat to etouffee and continue to cook another 30 minutes, until sauce is thickened and flavorful and chicken is beginning to fall apart. Add chopped parsley and stir well to combine. Taste and adjust seasoning, if necessary, and serve immediately over rice or other starch of choice.