Slice each chicken breast in half lengthwise to make 4 thinner cutlets and season both sides with salt, pepper, and garlic powder.
Heat the olive oil and butter in a large skillet over medium‑high heat until the butter melts and the pan is hot.
Add the chicken to the skillet and cook 5–6 minutes per side, or until nicely seared and an instant‑read thermometer reads 165°F (74°C); transfer to a plate and tent loosely with foil.
Return the skillet to medium‑high heat and add the flour, oregano, and minced garlic; cook, stirring, about 1 minute to remove the raw flour taste.
Pour in the chicken broth and whisk, scraping any brown bits from the pan, and cook until the liquid reduces by about half.
Reduce heat to medium, stir in the heavy cream, and simmer 6–7 minutes until the sauce thickens slightly.
Stir in the shredded Parmesan until melted and the sauce is smooth.
Return the chicken and any accumulated juices to the skillet, spoon sauce over each piece, and cook 2–3 minutes to reheat and meld flavors; sprinkle with chopped parsley.
Let the chicken rest 2 minutes before serving.