Start by trimming any excess fat from the chicken breasts. Place each breast between two sheets of plastic wrap or parchment paper and gently pound them to an even thickness, about 1/2 inch. In a shallow bowl, combine the flour, garlic powder, salt, and pepper. Dredge each cutlet in the flour mixture, shaking off any excess.
Heat the olive oil in a large skillet over medium-high heat. Once hot, add the chicken cutlets and cook for 3–4 minutes on each side until golden brown and cooked through. Remove the chicken from the skillet and set aside on a plate, tented with foil to keep warm.
Reduce the heat to medium and add the butter to the same skillet. Once melted, add the sliced mushrooms and sprinkle with salt. Cook, stirring occasionally, for about 5–7 minutes until the mushrooms release their moisture and turn golden brown. Add the pressed garlic and cook for an additional 1–2 minutes until fragrant.
Pour the heavy cream into the skillet with the mushrooms. Stir to combine and bring the mixture to a gentle simmer. Allow the cream to reduce slightly, thickening the sauce, about 5 minutes. Stir in the grated parmesan cheese until melted and smooth. Taste and adjust seasoning if needed.
Return the cooked chicken cutlets to the skillet, nestling them into the mushroom cream sauce. Spoon the sauce over the chicken and warm everything through for 2–3 minutes. Serve immediately with your favorite sides.