Begin by patting the chicken breasts dry with paper towels. Season both sides with salt, pepper, and garlic powder, and then lightly coat them in flour, shaking off any excess.
In a large skillet, heat the olive oil and butter over medium-high heat. Once hot, add the chicken cutlets in a single layer. Cook for about 4-5 minutes on each side until they are golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the sliced mushrooms. Cook them for about 5-7 minutes until they are browned and have released their moisture. Stir in the pressed garlic and an additional 1/2 tsp of salt. Sauté for another minute until fragrant.
Reduce the heat to medium and pour in the heavy cream, stirring to combine with the mushrooms. Allow the mixture to simmer for about 4-5 minutes until it thickens slightly.
Stir in the grated parmesan cheese until melted and creamy. Taste the sauce and adjust seasoning if necessary.
Return the chicken cutlets to the skillet, spooning the creamy mushroom sauce over them. Allow everything to simmer together for an additional 2-3 minutes to meld the flavors. Serve warm, garnished with fresh parsley or thyme if desired.
