Pat the chicken cutlets dry. Season both sides with salt, black pepper, and garlic powder, then lightly dredge in the flour and shake off the excess.

Heat the olive oil and butter in a large skillet over medium-high heat. Add the chicken cutlets and sear for 4 to 5 minutes per side until golden brown and nearly cooked through. Transfer to a plate.

Reduce the heat to medium. Add the sliced mushrooms to the same skillet and cook for 6 to 8 minutes, stirring occasionally, until browned and tender.

Add the chopped shallot and minced garlic. Cook for 1 minute until fragrant.

Pour in the chicken broth and scrape up the browned bits from the bottom of the skillet. Stir in the Dijon mustard and dried thyme, then simmer for 2 to 3 minutes.

Lower the heat and stir in the heavy cream and grated Parmesan. Simmer gently for 2 to 3 minutes, stirring often, until the sauce is smooth and slightly thickened.

Return the chicken and any juices to the skillet. Spoon some sauce over the top and simmer for 3 to 5 minutes, until the chicken is fully cooked and reaches 165°F.

Taste and adjust with additional salt and black pepper if needed. Sprinkle with chopped parsley and serve warm.