In a shallow bowl, combine flour, parmesan cheese, garlic powder, salt, and pepper. Dredge chicken in flour mixture to coat completely. Shake off any excess.
Place a large skillet over medium-high heat. Add olive oil and butter.
Once butter is melted, add chicken to the skillet. Cook for 3-5 minutes on each side until cooked through and golden brown.
Remove chicken to a plate and set aside.
To the same skillet add the chopped onion and cook until translucent, about 5-7 minuts.
Add garlic and saute until soft and fragrant. Add a little chicken broth to deglaze the pan, being sure to scrape up the brown bits on the bottom of the pan.
Add the remaining broth and heavy cream to the skillet. Cook until simmering and then reduce heat to medium. Stir often until the sauce has thickened.
Add grated Parmesan cheese to the sauce and stir until melted. Season to taste with salt and pepper.
Return chicken to the pan along with any resting juices on the plate. Cook for 2 minutes, spooning sauce over the chicken as it cooks.
Sprinkle with chopped parsley and a little extra Parmesan cheese. Serve warm.
Notes
You could also buy two regular boneless skinless chicken breasts and cut them in half to make 4 thin breasts.