Use a pan that can go from the oven to the stovetop. A roasting pan, large skillet or sauté pan are ideal for braising the chicken in the oven then placing on the stove to finish the sauce.
Pat the chicken breasts dry and season both sides with the kosher salt and black pepper.
Spread half the mustard on one side of the chicken, transfer to a dish, mustard side down and spread the remaining mustard over the top of the chicken breasts. Cover and refrigerate for at least one hour.
Toss the parsley, basil, tarragon and garlic cloves into the bowl of a food processor. Process until the herbs and garlic are finely chopped.
Whisk together 1 cup of the chicken stock with the wine vinegar and pour it into a large skillet that has been lightly sprayed with a cooking spray. Stir in half of the herb and garlic blend.
Place the chicken breasts in a roasting pan and scatter the remaining herb and garlic blend over the top of the chicken.
Cover the pan and bake in a 375-degree oven for 40 to 50 minutes, or until the chicken breasts are cooked through to an internal temperature of 165-degrees.
Remove the chicken from the pan and cover tightly with foil while you cook the pasta and finish the sauce.
Place the roasting pan over medium heat. Whisk together 1 tablespoon of the remaining chicken stock and the cornstarch. Pour the cornstarch and the cream into the cooking liquid, whisking to blend together. Continue cooking until the sauce begins to thicken slightly, about 10 to 15 minutes.
While the sauce thickens, heat the remaining chicken stock in a shallow stockpot. Add the concentrated chicken stock and the fettuccini. Cook until the pasta is just tender and most of the stock has been absorbed. Stir frequently as the stock is absorbed to prevent the pasta from sticking to the pan.
Transfer the pasta and any remaining stock to the roasting pan, stirring to coat the fettuccini.
Serve the fettuccini with the mustard and herb braised chicken.