Begin by placing the chicken breasts between two sheets of plastic wrap. Use a meat mallet to pound them to an even thickness, about 1/2 inch. Season both sides with garlic powder, salt, and pepper.
On a large plate, combine the flour with 1/2 teaspoon of salt. Dredge each chicken cutlet in the flour mixture, shaking off any excess.
In a large skillet over medium-high heat, add the olive oil and butter. Once the butter has melted and is bubbling, add the chicken cutlets in a single layer. Cook for 3-4 minutes on each side or until golden brown and cooked through. Remove the chicken from the skillet and set aside on a plate.
In the same skillet, add the sliced mushrooms. Sauté for about 5 minutes, or until they are browned and have released most of their moisture. Add the pressed garlic and sauté for an additional 1-2 minutes until fragrant.
Pour in the heavy cream and stir to combine, scraping up any browned bits from the bottom of the skillet. Add the grated parmesan cheese and stir until melted and the sauce thickens slightly. Season with an additional 1/2 teaspoon of salt, adjusting to taste.
Return the chicken to the skillet, spooning the mushroom cream sauce over the top. Let everything simmer together for a few minutes to meld the flavors. Serve hot, garnished with fresh parsley if desired.
