There are lots of ways to make this dish. You could use whole fresh tomatoes, you could eliminate the cream and you could make it complicated by using multiple pans. I haven't done any of these but what I have done is keep the recipe simple and straight forward which in the end creates a rewarding and satisfying comfort food. I rarely cook anything other then a whole chicken, whether left whole or cut into pieces. Thighs would be great for this as would (I have put my hands over my eyes ) boneless skinless chicken breasts. If you use the breasts be very mindful of your cooking time or you will dry them out. —thirschfeld
Season the chicken with salt and white pepper. Place a heavy bottom 12" skillet over medium high heat. When the pan is hot add enough olive oil to form a thin film on the bottom of the pan. Add the chicken skin side down. Brown the chicken to your liking.
When the chicken is brown quickly remove it to a plate. Add the butter and the shallots to the sauté pan. Saute the shallots until golden.
Deglaze the pan with the white wine and let the wine reduce to a tablespoon or so. Add the chicken stock, tomato paste and the sprigs of tarragon. Place the chicken back into the pan and let the sauce come to a boil. Reduce the heat to a simmer.
Place a lid on the pan and simmer the chicken until tender. About thirty minutes. Mean while heat the oven broiler.
When the chicken is tender remove the lid from the pan. Carefully place the pan into the oven under the broiler and broil it for 3 to 5 minutes or however much time it takes to crisp up the skin. Remove from the oven.
Remove the chicken to a platter. Place the pan over high heat. Add the cream and stir it in. Add the chopped tarragon. Taste the sauce and adjust the seasoning. Stir and bring to a boil.
Sauce the chicken and serve over rice with extra sauce on the side.