Massage the olive oil on the outside; season very well with paprika, salt and pepper. Rub the seasoning all over the chicken. Place on a foil lined baking sheet. Bake in the oven to an internal temperature of 160 degrees using a thermometer. (Wings will be done before the thigh and drumstick)Make sure to probe the thickest part of the muscle away from a bone to get an accurate reading on the thermometer.
Add any juice from the chicken into a saucepan on medium heat. Stir in the broth, thyme, butter and bring to a simmer. Whisk in the flour slurry a little at a time until the gravy thickens to a creamy consistency. Season with salt to taste.
Serve the chicken. Spoon the gravy over the mashed potatoes. Garnish with parsley.