Preheat oven to 400 degrees. Rinse chicken thoroughly inside and out. Pat dry. Sprinkle chicken inside with salt and pepper. Place tarragon sprigs in cavity. Rub butter all over outside of chicken. Place chicken in roasting pan. Sprinkle with salt and pepper. Pour 1/2 cup water into roasting pan.
Roast chicken until thermometer inserted into thickest part of thigh registers 175 degrees and juices run clear when thigh is pierced, basting occasionally with juices from pan, about 1 hour. Transfer chicken to platter, cover with foil while making sauce.
Transfer pan juices to medium saucepan. Freeze until fat rises to the top, about 10 minutes. Spoon off fat, discard. Add vermouth to pan juices in saucepan. Boil until slightly reduced, about 3 minutes. Add cream and tarragon and boil until mixture thickens to sauce consistency, stirring occasionally, about 5 minutes. Whisk egg yolks in a bowl. Temper the yolks with cream sauce. Return the yolk mixture to the rest of the sauce. Season sauce with salt and pepper. Serve with chicken.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.