Season chicken cutlets on both sides with salt and pepper.
Heat olive oil in a large skillet over medium-high heat.
Sear the chicken for 4 to 5 minutes per side until golden brown and internal temperature reaches 165 degrees Fahrenheit. Remove chicken from the skillet and set aside.
In the same skillet, add sliced mushrooms and sauté for 5 to 7 minutes until moisture evaporates and they turn golden brown.
Add minced garlic and dried thyme to the mushrooms; sauté for 60 seconds until fragrant.
Deglaze the skillet with chicken broth, scraping the browned bits from the bottom of the pan.
Stir in the heavy cream and bring to a gentle simmer over medium heat.
Whisk in the grated Parmesan cheese and continue to simmer for 2 to 3 minutes until the sauce thickens slightly.
Return the cooked chicken to the skillet, spooning the sauce over the meat to coat thoroughly.
Garnish with chopped parsley and serve immediately.