This is a simple dish to prepare, which is a real plus for all you busy parents with hectic week-night schedules. And I think--or at least I hope--you'll agree that the combination of ingredients form a well-rounded taste sensation with a delectable tarragon cream sauce to serve over your tender chicken breasts. And you can even use the extra sauce to drizzle over a side dish of fresh asparagus or other vegetable dish. Prep time is primarily the marinating time, which can be reduced if you're in a hurry.
In a small bowl, mix together the 2 tablespoons Dijon mustard and 1/2 tablespoon tarragon leaves. Rub the mixture over the chicken breasts. Place chicken breasts in a covered dish (or in a plastic zip-lock bag) and keep chilled in the refrigerator for at least 3 hours.
Heat the olive oil in a skillet over medium heat.
Meanwhile, add the flour to a shallow dish; season flour with salt and pepper, to taste. Dredge the chicken in the seasoned flour. Brown the chicken on both sides in the heated skillet. Cover, and continue cooking the chicken for about 15 minutes, turn and cook other side about 10 minutes or until chicken is thoroughly cooked and juices run clear. Transfer chicken to a platter, and keep warm.
In the same skillet, sauté the minced shallots (or red onion), garlic, and mushroom slices for about 3 or 4 minutes or until onions are soft.
Deglaze the pan by adding the wine, cream, mustard and tarragon to the onion/garlic mixture. Stir frequently, scraping the pan to loosen bits of chicken that might remain, and cook for 5 minutes or until the sauce begins to thicken. Return chicken to skillet just long enough (about a minute or so) to coat with the cream sauce.
Place chicken breasts on individual plates, and drizzle remaining sauce over the chicken.