Prepare the Chicken: Pat the chicken breasts dry and season them all over with 1½ teaspoons of salt.
Brown the Chicken: Heat 1 tablespoon of olive oil in a large skillet over medium heat. When the oil is hot and shimmering, add the chicken breasts. Cook for about 5 minutes per side, or until they are golden brown. Transfer the chicken to a plate and set aside.
Make the Sauce: In the same skillet, add the remaining tablespoon of oil and the sliced shallots. Cook, stirring, until the shallots are tender, about 4 minutes. Add the minced garlic and cook for about 30 seconds, until fragrant. Pour in the white wine and cook until it has reduced by half, about 4 minutes, scraping up any browned bits from the bottom of the pan with a wooden spoon.
Add Cream and Flavorings: Stir in the heavy cream, chicken stock, chicken Better than Bouillon, 2 tablespoons of fresh tarragon, Dijon mustard, lemon zest, and the remaining ¼ teaspoon salt. Mix well.
Simmer the Chicken: Return the chicken to the skillet along with any juices from the plate. Bring the sauce to a simmer over high heat, then reduce the heat to medium-low. Let it simmer until the chicken reaches an internal temperature of 165°F (74°C) on an instant-read thermometer, about 15 minutes.
Thicken the Sauce: In a small bowl, mix the cornstarch with 2 tablespoons of cool water to make a slurry. Remove the chicken from the skillet and set aside. Pour the cornstarch slurry into the sauce and continue to simmer until the sauce has thickened, about 3 minutes. Return the chicken to the skillet and coat it with the sauce.
Finish and Serve: Sprinkle the chicken with freshly cracked black pepper and the remaining 1 tablespoon of chopped tarragon. Serve over cooked pasta or mashed potatoes, if desired.