Slice chicken breasts in half horizontally to create thinner cutlets.
In a shallow dish, mix flour, salt, and black pepper.
Dredge the chicken cutlets in the flour mixture, shaking off excess.
Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat.
Add chicken cutlets and cook for about 4-5 minutes per side until golden and cooked through. Remove and set aside.
In the same skillet, melt remaining butter.
Add sliced mushrooms and sauté until browned and tender, about 5 minutes.
Pour in Marsala wine and scrape up any browned bits from the skillet.
Let the wine simmer for 2-3 minutes to reduce slightly.
Add chicken broth, garlic powder, dried thyme, and stir well.
Pour in heavy cream, stirring until the sauce thickens (about 3-4 minutes).
Return the chicken cutlets to the skillet, spoon sauce over them, and simmer for another 2-3 minutes.
Garnish with chopped parsley and serve hot.