Season chicken halves with salt and pepper on both sides.
Heat olive oil in a large skillet over medium-high heat.
Add chicken to the skillet and sear for 5 to 7 minutes per side until golden brown and the internal temperature reaches 165 degrees Fahrenheit.
Remove chicken from the skillet and set aside on a plate.
In the same skillet, add the sliced mushrooms and sauté for 5 minutes until browned and moisture has evaporated.
Add minced garlic and cook for 60 seconds until fragrant.
Pour in the chicken broth and heavy cream, scraping any browned bits from the bottom of the pan.
Simmer the sauce for 3 to 5 minutes until it begins to thicken.
Stir in the Parmesan cheese and dried thyme until the cheese is melted and the sauce is smooth.
Return the chicken to the skillet, spooning the sauce over the meat, and garnish with fresh parsley before serving.