Prepare the Chicken: Pat the chicken breasts dry with paper towels and season generously with salt and pepper on both sides.
Sear the Chicken: Heat the olive oil in a large skillet over medium-high heat. Add the chicken breasts and sear for 4–5 minutes per side, or until golden brown. Remove the chicken from the skillet and set aside.
Sauté the Vegetables : In the same skillet, add the sliced mushrooms and chopped onion. Cook for 5–7 minutes, stirring occasionally, until softened and lightly browned. Stir in the minced garlic and cook for another 1–2 minutes, until fragrant.
Make the Cream Sauce: Reduce the heat to medium. Pour in the chicken broth, scraping the bottom of the skillet to deglaze. Stir in the heavy cream and thyme, and let the mixture simmer for 2–3 minutes.
Return the Chicken: Return the chicken breasts to the skillet, nestling them into the sauce. Simmer for 10–12 minutes, or until the chicken is cooked through (internal temperature of 165°F/74°C).
Add Finishing Touches: Stir in the grated Parmesan cheese (if using) until melted and combined Garnish with fresh parsley before serving.