To make the herb butter, put 1 stick plus 6 tablespoons of the butter in a bowl and beat it with a spoon (or do this in a mixer) until smooth and creamy. Chop ¾ of the parsley and chervil leaves and all of the tarragon and blend with the butter. Save the remaining parsley and chervil sprigs for garnishing the plates.
Cook the chopped mushrooms in the remaining 6 tablespoons butter in a sauté pan over medium heat until soft, about 6 minutes. Season with salt and pepper, remove from the heat, and let cool. Add the cooled mushrooms and the shallot slices to the herb butter and mix thoroughly.
Preheat the oven to 350°F. Starting at the back end of the chicken breast, slip your fingers under the skin and carefully lift it from the flesh of the chicken without tearing it. When both sides of the breast have been separated, spread the herb butter evenly between the skin and the flesh of the breast meat. Pull the skin back over the breast.
Either spit-roast or bake the chicken in the oven for 45 minutes. Pour the chicken stock over the chicken and roast, basting occasionally with the pan juices, for 45 minutes longer, or until the thigh juices run clear when pierced near the bone.
Let the chicken rest for about 10 minutes. Skim the fat off the pan juices. Carve the chicken and serve with the pan juices.