How to Make It
In a large nonstick skillet, heat the oil until shimmering. Season the chicken with salt and pepper, add to the skillet and cook over moderately high heat, turning once, until browned, about 3 minutes per side. Transfer the chicken to a plate.
Add the butter, shallot, salt and mushrooms to the skillet and cook, stirring frequently, until the mushrooms begin to brown, about 12 minutes. Add the flour and cook until it smells lightly toasty, about 1 minute.
Add the wine, broth and reserved chicken and bring to a simmer. Cover and cook over moderate heat until the chicken is cooked through, about 5 minutes. Transfer the chicken to a serving dish.
Increase the heat to moderately high and simmer the sauce, uncovered, until slightly reduced, about 5 minutes. Remove the skillet from the heat and stir in the minced tarragon and heavy cream. Spoon the sauce and mushrooms over the chicken and serve immediately.
Tip: Swap out the mushrooms for leeks for a lighter flavored dish. Tip: Chop any leftover chicken and mushrooms and serve as a sauce over pasta or polenta. One serving: 396 cal, 14 gm fat, 4.5 gm sat fat, 12 gm carb, 2 gm fiber, 51 gm protein.