Begin by patting the chicken breasts dry and cutting them into even cutlets, ensuring uniform thickness for consistent cooking.

In a shallow bowl, combine all-purpose flour with salt, pepper, and garlic powder. Dredge each chicken cutlet in this mixture.

Heat a large skillet over medium heat, add unsalted butter and olive oil, then brown the chicken cutlets for about 5 minutes on each side.

In the same skillet, add the remaining unsalted butter and toss in the sliced mushrooms. Sauté for about 6 to 8 minutes.

Add chopped shallots to the skillet and cook until softened, then stir in minced garlic and sauté for 30 seconds.

Pour in dry white wine, scraping up any brown bits from the pan, and let it simmer for about 2 minutes.

Stir in chicken broth, fresh thyme, Dijon mustard, and heavy cream. Bring to a simmer for about 5 minutes.

Dissolve cornstarch in cold water to create a slurry and stir into the sauce, then return the chicken to the skillet.

Simmer for an additional 5 minutes, or until the sauce thickens to your desired consistency. Adjust seasoning and serve.