Pat the chicken cutlets dry and, if needed, pound them to an even thickness for consistent cooking.

In a shallow bowl, mix together the flour, salt, pepper, and garlic powder. Dredge each chicken piece in the flour mixture and shake off the excess.

In a large skillet over medium heat, melt 2 tablespoons of butter with 1 tablespoon of olive oil. Brown the chicken in batches for about 5 minutes per side. Transfer to a plate and keep warm.

Add the remaining 2 tablespoons of butter to the skillet. Place the mushrooms in a single layer and let them cook undisturbed until one side is deeply browned. Flip and continue cooking until their liquid releases and evaporates.

Stir in the sliced shallots and cook until soft. Add the garlic and sauté for another 30 seconds until fragrant.

Pour in the white wine and use a spatula to scrape up the browned bits from the bottom of the pan. Add thyme sprigs, chicken broth, Dijon mustard, and heavy cream. Let the mixture simmer for 5 minutes.

Stir in the cornstarch slurry and return the chicken to the pan. Simmer everything for about 5 more minutes, or until the sauce thickens and the chicken is fully cooked.

Remove thyme sprigs, taste the sauce, and adjust seasoning with more salt or pepper as needed. Optionally garnish with fresh parsley or thyme and serve hot.