Season the chicken breasts generously with salt and pepper on both sides.
Heat the olive oil and butter in a large skillet over medium-high heat.
Sear the chicken breasts for 5-7 minutes per side until golden brown and cooked through (internal temperature reaches 165°F). Remove the chicken from the skillet and set aside on a plate, keeping it warm.
Add the sliced mushrooms to the same skillet. Cook, stirring occasionally, until they release their moisture and start to brown, about 5-7 minutes.
Add the minced garlic and dried thyme to the skillet. Cook for 1 minute until fragrant.
If using wine, pour it into the skillet to deglaze, scraping up any browned bits from the bottom. Let the wine reduce by half.
Pour in the chicken broth and bring the mixture to a simmer. Cook for 3 minutes until the liquid slightly thickens.
Reduce the heat to low. Stir in the heavy cream and grated Parmesan cheese. Continue stirring until the cheese melts and the sauce is smooth and creamy. Do not let the sauce boil after adding the cream.
Return the cooked chicken breasts to the skillet, spooning the sauce over them. Heat through for 1-2 minutes.
Garnish with fresh chopped parsley before serving.
Notes
For a richer flavor, use chicken thighs instead of breasts. Adjust cooking time as needed.
If you prefer not to use dairy cream, substitute with full-fat coconut milk for a similar texture, though the flavor profile will change slightly.
If you do not have white wine, use an equal amount of chicken broth for deglazing.
Serve this dish over pasta, rice, or creamy mashed potatoes to soak up the sauce.