Combine the garlic salt, Herbes de Provence, flour, sugar, and pepper in a small bowl and stir to combine. Set aside.

Cut the chicken breasts in half horizontally and sprinkle on both sides with the garlic salt mixture.

In a large skillet, melt the butter with the olive oil over medium heat until starting to sizzle.

Add the chicken breasts, smooth sides down, and cook for 4-6 minutes or until the underside is golden. Flip and cook for another minute. Transfer to a clean plate and cover loosely with foil.

Add the chopped shallots to the pan and sauté over medium-low heat for 1-2 minutes until softened. Add the garlic and sauté for another 30 seconds.

Add the wine and increase the heat to medium-high. Cook until most of the wine has evaporated.

Add the chicken broth and bay leaves, bringing the mixture to a steady low boil. Cook uncovered for 8 minutes.

While the broth is cooking, combine the cream, mustard, and cornstarch until smooth.

(Optional) Strain the mixture through a fine mesh strainer to achieve a smoother sauce. Discard the solids, return the sauce to the pan, and bring to a boil.

Add the cream mixture and any accumulated chicken juices to the pan, stirring until well combined. Bring back to a boil, then reduce to a slow simmer over low heat and cook for 2 minutes, stirring frequently.

Remove the bay leaves and discard them. Taste and add additional salt and pepper, if needed.

Add the chicken back to the pan, cover tightly, and turn off the heat. Let sit undisturbed for 5 minutes. Serve drizzled with sauce and garnish with dill, thyme, or rosemary.