In a shallow bowl, combine flour, salt, and pepper. Dredge chicken pieces until evenly coated, shaking off any excess flour.
Heat olive oil in a large skillet over medium-high heat. Sear chicken for 5 to 7 minutes per side until golden brown and the internal temperature reaches 165 degrees Fahrenheit. Remove chicken and set aside on a plate.
In the same skillet, melt the butter over medium heat. Add minced garlic and sauté for approximately 1 minute until fragrant, being careful not to burn it.
Deglaze the pan with chicken broth, scraping the bottom of the pan with a wooden spoon to release the browned bits. Simmer for 2 minutes.
Reduce heat to medium-low. Stir in the heavy cream, Parmesan cheese, dried oregano, and red pepper flakes. Simmer for 3 to 5 minutes, stirring frequently, until the sauce has thickened slightly.
Return the chicken cutlets to the skillet. Spoon the sauce over the chicken and simmer for an additional 2 minutes to ensure the meat is heated through.
Garnish with fresh parsley and serve immediately.