Season chicken breasts with salt and pepper on both sides.
Heat olive oil in a large skillet over medium-high heat.
Sear chicken for 5 to 7 minutes per side until golden brown and internal temperature reaches 165°F (74°C). Remove chicken from skillet and set aside.
In the same skillet, melt butter and add sliced mushrooms. Sauté for 5 minutes until browned and moisture has evaporated.
Add minced garlic and cook for 60 seconds until fragrant.
Deglaze the pan with chicken broth, scraping the bottom to release fond.
Whisk in heavy cream, parmesan cheese, oregano, and red pepper flakes. Simmer for 3 to 5 minutes until the sauce has thickened to a coat-the-back-of-a-spoon consistency.
Return chicken to the skillet, spooning the sauce over the meat.
Garnish with fresh parsley and serve immediately.