Sprinkle salt and pepper over both sides of the chicken breasts to season them well.

Heat a skillet over medium-high heat, then melt 1 tablespoon of butter and add the olive oil. Place the seasoned chicken breasts into the skillet and sear until each side is golden brown, about 4-5 minutes per side. Remove the chicken and set it aside on a plate.

Deglaze the skillet by pouring in the chicken broth, scraping up any browned bits from the bottom. Cook for about 30 seconds, or until most of the liquid has evaporated.

In the same skillet, add the remaining 1 tablespoon of butter and sauté the mushrooms until they're soft and the liquid has reduced, approximately 5 minutes.

Add the minced garlic to the skillet and sauté for about 30 seconds until it's fragrant.

Sprinkle the flour into the skillet and cook, stirring constantly for about 1 minute to eliminate the raw flour taste.

Lower the heat to medium-low, then pour in the chicken broth and heavy cream. Bring the mixture to a gentle boil. Gradually add the Parmesan cheese in batches, stirring continuously until it melts completely and creates a smooth sauce.

Taste the sauce and adjust the seasoning with additional salt and pepper if necessary.

Allow the sauce to simmer gently, reducing slightly until it becomes thick and creamy, about 2-3 minutes.

Return the chicken breasts and any collected juices back to the skillet. Simmer for another 2 minutes or until the chicken is warmed through and the internal temperature reaches 165°F.

Garnish with fresh chopped parsley or chives (optional) and serve the dish hot.

Enjoy!