Using some of the butter, grease a large roasting pan well.
Then preheat oven to 375°F (190°C).
Roughly chop all vegetables (if you don't they might cook down too much or get mushy).
In large bowl combine all vegetables. Sprinkle with olive oil, pepper flakes, garlic powder, and 1 tablespoon tarragon. Set aside.
Pat chicken dry, making sure no innards are left in the chicken. Sprinkle 1 tablespoon tarragon inside of chicken along with a pinch of salt and pepper.
Carefully mix remaining butter and tarragon place it under the skin of the chicken on top of the breasts.
Place a small oven-safe grate or rack in bottom of roasting pan then pour in your mixed vegetables. Around it add ½ cup chicken stock.
Place chicken on top of rack so it sits above the vegetables and stock.
Cover with either lid or aluminum foil. Place in oven, adding ½ cup chicken stock as needed to keep the vegetables moist, but not drowned. Cook chicken for 2 hrs( cooking times vary on size of chicken and oven settings). Once chicken is close to being done, pull from oven and remove cover. Sprinkle with ground cayenne pepper and salt.
Place chicken back into oven to brown for 10-15 minutes.