1- 1 ½ lbs small new potatoes (fingerling would be a good choice)
Clean the chicken and dab it dry with paper towel. Rub inside and out with kosher salt and freshly ground pepper. Take a couple of sprigs of each parsley and tarragon, chop them coarsely, stuff them into the empty cavity. Freeze or dispose of liver. But hold on to the neck and gizzards. Melt the butter in a pot big enough to hold the chicken and the cream and stock. When the butter begins to brown, in goes the chicken, the neck and the gizzards. Brown on all sides. When nice and browned, add about ¾ of the cup of cream and all of the chicken stock. Stir to mix. While this all comes to a boil, chop the rest of the parsley and tarragon-except for a couple of sprigs for decorating-finely. When the liquids surrounding the chicken come to a boil, add the herbs, stir again, turn to low, put on a lid and let simmer away for about and hour and a half. You want the chicken to cook until it literally falls apart.
Scrub the potatoes and put them in a pot with water just to cover and kosher salt. About a half an hour before the chicken is ready to serve, turn on the potatoes and let boil under lid for about fifteen minutes. At about twelve minutes, start testing for doneness. You want them cooked through but still al dente – with firmness to the bite. Obviously, you want potatoes and chicken to be ready at the same time.
When the chicken is just about falling apart, transfer to a dish or bowl while you boil down the liquids in the pot. Reduce to about half or slightly less. If there’s a lot of fat on top, skim it off. The sauce should be thick and velvety. You may want to add the last quarter cup of cream to help the sauce thicken and get the right degree of velvetiness. Discard gizzards and neck.
Check sauce to see if it needs more salt or pepper, when it’s ready, put the chicken back in for a couple of minutes to reheat. Then transfer to a cutting board. Cut in serving pieces, place on a platter or serving dish. If you have one that is large enough to also hold the potatoes, more power to you. Sprinkle with coarsely chopped parsley and tarragon. Serve!