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.