1. Heat olive oil in a large skillet over medium-high heat. Season the chicken breasts with salt and pepper, then add them to the skillet. Cook for about 5-7 minutes on each side until golden brown and cooked through. Transfer the chicken to a plate and set aside.
2. In the same skillet, melt the butter over medium heat. Add the sliced mushrooms and cook until they are golden and tender, about 5 minutes. Stir in the minced garlic and cook for an additional minute until fragrant.
3. Pour in the chicken broth, scraping up any browned bits from the bottom of the skillet. Allow it to simmer for 2-3 minutes to reduce slightly.
4. Reduce the heat to low and stir in the heavy cream and thyme. Let the mixture simmer gently until it thickens, about 5 minutes.
5. Return the chicken to the skillet, spooning the creamy sauce over the top. Let it cook for another 2-3 minutes to warm through.
6. Stir in the Parmesan cheese until melted and the sauce is smooth and creamy. Garnish with fresh parsley before serving, if desired.

Remember, patience is key! Letting the sauce simmer allows the flavors to meld beautifully, much like those hours spent in my abuela’s kitchen.