Season both sides of the chicken fillets with salt and black pepper.
Heat olive oil in a large stainless steel or cast iron skillet over medium-high heat.
Sear the chicken fillets for 5-6 minutes per side until the internal temperature reaches 74°C (165°F) and the surface is golden brown.
Remove chicken from the skillet and set aside on a warm plate.
Add butter to the same skillet over medium heat. Once foaming, add sliced mushrooms and sauté for 6-8 minutes until the moisture has evaporated and mushrooms are deeply browned.
Add minced garlic and cook for 1 minute until fragrant.
Deglaze the skillet with white wine or chicken stock, scraping the bottom of the pan to incorporate the fond.
Stir in heavy cream and thyme. Simmer for 3-5 minutes until the sauce reduces and achieves a nappe consistency.
Return the chicken fillets and any accumulated juices to the pan. Spoon the sauce over the fillets to coat.
Garnish with fresh parsley and serve immediately.