Rinse chicken and pat dry, season with salt inside and out. Place on a rimmed dish and chill uncovered, 4 hours or overnight in lowest part of refrigerator.
Pat chicken dry again and season with a little pepper. Stuff the chicken with the whole bundle of parsley, fresh bay leaves and the onion. Tie legs with string to secure cavity and close shut.
In a large Dutch oven, melt butter over medium to medium-high heat. Add chicken and brown evenly all over, 15 minutes or so. Reduce heat and cover; cook 50-60 minutes, turning occasionally, until juices run clear.
When chicken is 10-15 minutes from the end of its cooking time, place potatoes in pot and cover with water. Bring to a boil, season with salt and cook to just tender. Drain and return potatoes to the hot pot.
Remove chicken to a cutting board. Cut away kitchen twine, discard onion and bay, and place the parsley bundle on the side of a serving platter. Carve chicken into pieces with cleaver or kitchen shears. Cover with foil to stay warm.
Whisk flour into chicken drippings over medium heat. Whisk in honey and stock, and let thicken a bit. Add chopped parsley.
Pour half of the sauce over the potatoes and half over the chicken, and serve.