Season the Chicken: Season the chicken fillets evenly with garlic powder, salt, and cracked pepper.
Dredge in Flour: Coat each chicken fillet in flour, shaking off any excess, then set the coated chicken aside.
Heat the Pan: Heat 1 tablespoon butter and the olive oil in a large skillet over medium-high heat until hot.
Sear the Chicken: Add the chicken and cook for about 3–4 minutes per side, depending on thickness, until golden on both sides and just cooked through.
Set Chicken Aside: Transfer the cooked chicken to a warm plate and keep it aside while preparing the sauce.
Sauté the Shallot: Add the remaining 2 tablespoons butter to the same skillet. Cook the chopped shallot for about 4 minutes, stirring occasionally, until softened.
Cook the Garlic: Add the minced garlic and sauté for about 1 minute, until fragrant.
Deglaze the Pan: Pour in the dry white wine or chicken broth, then use the end of a wooden spoon to scrape the browned bits from the bottom of the skillet.
Reduce the Wine: Bring the liquid to a simmer and cook for about 4 minutes, or until it has reduced by half.
Add the Mustard: Stir the Dijon mustard into the pan juices until incorporated.
Add Broth and Herbs: Pour in the chicken broth and add the chopped tarragon, dried thyme, and chopped rosemary. Bring the mixture to a boil.
Simmer the Sauce: Reduce the heat to medium, stir in the heavy cream, and simmer for about 3 minutes, until the sauce begins to thicken.
Return the Chicken: Place the cooked chicken back into the skillet, coating it with the sauce.
Finish Cooking: Gently simmer the chicken for about 5 minutes, until heated through and the sauce has thickened.
Adjust the Seasoning: Taste the sauce and add salt and cracked pepper as desired.
Serve: Serve the chicken with the creamy mustard sauce spooned over or alongside the fillets.
