Chicken and tarragon (estragon in French) are a match made in heaven. The flavor is very subtle but delicious. I cooked chicken this way over the weekend, using sprigs of fresh tarragon from a potted plant that I've managed to keep going for two or three years now.
I had bought a whole chicken — a corn-fed poulet jaune — and I decided to cook just half of it for the two of us. I cut it in half along one side of the backbone and through the breastbone, and I put the half with the backbone still attached in the freezer. Maybe we'll cook that on the grill later.
Poulet à l'estragon et au vin blanc — you could make the same thing using just chicken breast or thigh meat.
I cut the other half of the chicken into four pieces: the drumstick, the thigh, and the breast/wing split in half. The first step in making tarragon chicken is to brown the chicken, skin side down, in a frying pan with some butter and/or oil. Once the chicken pieces are golden brown, take them out of the pan and put them in a medium oven, covered, for 15 minutes to stay warm and continue cooking.
The second step is to make the sauce. Remove some of the fat from the frying pan if you think there's too much in there. Slice up a couple of shallots or a small onion and cook the slices lightly in the pan. When they are softened but not really browned, pour in half a cup of white wine and half a cup of chicken broth (or water). Stir well.
Let the tarragon sprigs and shallot slices "steep" in the sauce to give all their flavor.
Add three six-inch sprigs of tarragon into the liquid, along with a quarter-cup of cream and a teaspoon or two of Dijon mustard. Another option is to put in a teaspoon or two of white wine vinegar instead of mustard, but I think the Dijon mustard is tastier. Simmer the sauce for five minutes so that the tarragon flavor will have time to develop. Don't forget to add some salt and pepper, to taste.
The chicken isn't swimming in sauce — you just want a small amount.
There you've pretty much got it. Add more cream if you want a richer sauce, which will thicken slightly as it reduces. Then take the chicken pieces out of the oven and put them back in the pan. Put on a lid and let the chicken, which is nearly completely cooked by now, simmer and steam through in the sauce for five minutes. Cook it as done as you like it, actually.
Chicken, tarragon cream sauce, pasta (coquillettes), and steamed summer squash slices panned in butter.
The final step is to put the chicken and the sauce in a serving dish and sprinkle on some chopped tarragon leaves to give everything that good fresh flavor. Serve with rice or pasta. We had some tiny elbow macaroni and some steamed summer squash slices with ours.