Preheat the oven to 375°F (190°C).
Season the chicken breasts evenly with salt and black pepper.
Heat olive oil in a large oven-safe skillet over medium-high heat.
Sear the chicken for 3-5 minutes per side until golden brown, then remove from the skillet and set aside.
In the same skillet, melt the butter and add the mushrooms. Sauté for 5-7 minutes until the mushrooms have released their moisture and turned golden brown.
Add the minced garlic and dried thyme to the skillet, cooking for 60 seconds until fragrant.
Deglaze the pan with chicken broth, scraping up the browned bits from the bottom.
Stir in the heavy cream and bring to a gentle simmer over medium heat.
Whisk in the parmesan cheese until the sauce is smooth and slightly thickened.
Place the seared chicken breasts back into the skillet, spooning the sauce over them.
Transfer the skillet to the oven and bake for 15-20 minutes, or until the internal temperature of the chicken reaches 165°F (74°C).
Garnish with chopped fresh parsley before serving.