Pat the chicken dry

Season all over with 1½ teaspoons of the salt.Heat 1 tablespoon of the oil in a large skillet over medium

Once the oil is glistening, add the chicken and cook about 5 minutes per side, or until golden brown

Transfer the chicken to a plate.Add the remaining oil and shallots to the same skillet and cook, stirring, until tender, about 4 minutes

Stir in the garlic until fragrant, about 30 seconds

Stir in the wine and cook until reduced by half, about 4 minutes, scraping the browned bits from the bottom of the pan with a wooden spoon

Stir in the heavy cream, chicken stock, bouillon, 2 tablespoons fresh tarragon, mustard, lemon zest, and remaining ¼ teaspoon salt

Return the chicken to the skillet along with any collected juices on the plate

Bring the sauce to a simmer over high heat, then reduce the heat to medium low

Simmer until the internal temperature of the chicken reaches 165°F on an instant-read thermometer, about 15 minutes more.In a small bowl mix the cornstarch together with 2 tablespoons cool water

Transfer the chicken to a plate

Pour the cornstarch slurry into the sauce and continue to simmer until thickened, about 3 minutes

Nestle the chicken back into the sauce

Top chicken with pepper and remaining 1 tablespoon tarragon and serve over pasta or mashed potatoes, if desired.