Season the chicken breasts evenly with the salt, garlic powder, and black pepper.
Combine the all-purpose flour and grated Parmesan in a shallow dish. Coat each chicken breast thoroughly in the flour-Parmesan mixture, then gently shake away any loose excess.
Warm 2 tablespoons of the olive oil together with 1 tablespoon of butter in a large skillet set over medium-high heat. Swirl the skillet so the fat coats the cooking surface evenly.
Cook 2–3 chicken breasts at a time for approximately 4–5 minutes per side, depending on their thickness. Continue cooking until both sides are golden, the centers are fully cooked, and no pink remains.
Move the cooked chicken to a warm plate. If additional chicken remains, repeat the cooking process, adding more oil and butter when necessary. Place all finished chicken breasts together on the plate and reserve.
Lower the heat to medium and carefully wipe the skillet with a sheet of paper towel.
Add the diced onion to the remaining oil and pan juices. Sauté until the onion becomes tender and softened.
Using the blunt side of a knife, crush 6 whole garlic cloves. Add the remaining olive oil to the skillet and stir it through the onions.
Add the crushed garlic, along with any additional whole garlic cloves, and sauté for approximately 2–3 minutes, or until aromatic.
Pour the chicken broth into the skillet to deglaze the pan. Scrape the browned pieces from the bottom so they become incorporated into the sauce.
Allow the broth mixture to simmer until its volume has reduced by roughly half, approximately 5 minutes.
Lower the heat to medium-low and add the heavy cream. Bring the sauce to a mild simmer and cook for approximately 2–3 minutes so the ingredients and flavors combine.
Stir in the grated Parmesan cheese. Continue cooking gently for another 2–3 minutes, stirring from time to time, until the cheese has completely melted into the sauce.
Taste the cream sauce and adjust with additional salt and black pepper as desired.
Return the cooked chicken breasts to the skillet. Simmer them in the cream sauce for a further 2–3 minutes, allowing the chicken to absorb the sauce while the mixture thickens to the preferred consistency.
Transfer the creamy chicken to a serving platter once the sauce has thickened and thoroughly coated the chicken.
Finish with the chopped fresh parsley and a light scattering of freshly cracked black pepper. Serve with pasta, cauliflower mash, zucchini noodles, rice, or mashed potatoes.