Combine garlic salt, Herbes de Provence, flour, sugar, and pepper in a small bowl; set aside.

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

In a large skillet, melt butter with olive oil over medium heat. Add chicken breasts, smooth sides down, and cook for 4-6 minutes until golden. Flip and cook for an additional minute. Transfer to a plate and cover loosely with foil.

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

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

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

While the broth is cooking, combine cream, mustard, and cornstarch in a bowl and stir until smooth.

Optional: Strain the sauce through a fine mesh strainer to achieve smoothness, discarding solids, then return to the pan and bring to a boil.

Add the cream mixture and any juices from the chicken plate to the simmering sauce; stir to combine and bring back to a boil, then reduce to a slow simmer over low heat for 2 minutes, stirring frequently. Remove and discard bay leaves.

Taste the sauce and adjust salt and pepper if needed.

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