Prepare the Chicken: Season the chicken breasts generously with salt and pepper on both sides.
Cook the Chicken: In a large skillet, heat olive oil over medium-high heat. Add the chicken breasts and cook for about 6-7 minutes per side, or until golden brown and cooked through. Remove the chicken from the skillet and set aside.
Sauté the Mushrooms: In the same skillet, add the sliced mushrooms and sauté for 3-4 minutes until tender and browned. Add the minced garlic and cook for an additional 1 minute, until fragrant.
Make the Sauce: Pour in the half-and-half (or whole milk), stirring to combine with the mushrooms and garlic. Let it simmer for 2-3 minutes, allowing the sauce to thicken slightly. Stir in the grated Parmesan cheese and continue to cook until the sauce is smooth and creamy.
Combine and Serve: Return the chicken breasts to the skillet, spooning the sauce over the chicken. Let it simmer for another 2 minutes to heat the chicken through. Sprinkle with chopped parsley and serve immediately.