Pat the chicken breasts dry with paper towels before cutting each breast in half horizontally into two thinner cutlets.

In a shallow bowl, combine flour, salt, pepper, and garlic powder, mixing well before setting aside. Heat 2 tablespoons of butter alongside 1 tablespoon of olive oil over medium heat in a large skillet until melted.

Dredge three chicken cutlets in the flour mixture, coating both sides thoroughly while shaking off any excess flour before adding them to the skillet. Cook until well browned on one side, approximately five minutes, then turn them over and cook for an additional three to five minutes until fully cooked through.

Once all chicken cutlets are cooked, remove them from the skillet, covering them on a plate to keep warm. Add remaining butter to the pan until melted before adding sliced mushrooms; cook undisturbed until dark brown on one side before stirring to finish cooking.

Add thinly sliced shallots to the pan next, cooking until softened before adding minced garlic; sauté briefly until fragrant then deglaze with apple vinegar while scraping up any brown bits from below. Stir in thyme sprigs, chicken broth, mustard, and cream, bringing this mixture to a boil before simmering gently for five minutes.

Stir in dissolved cornstarch while returning sauce back to a light simmer; add previously cooked chicken back into the skillet as well to heat through while allowing flavors meld together for about five minutes or until thickened appropriately. Remove thyme sprigs from final dish, season with salt and pepper as desired before serving garnished with parsley or additional thyme alongside rice, potatoes or noodles.