Reduce heat to medium or medium-low and add the butter to the same skillet. As it melts, gently scrape up the browned bits from the bottom using a silicone spatula to incorporate flavor into the sauce.
Add the garlic cloves and cook, stirring occasionally, for 6–7 minutes until softened and lightly caramelized.
Sprinkle in the flour and cook for 1–2 minutes to eliminate any raw flour taste.
Slowly pour in the prepared broth mixture, stirring constantly to maintain a smooth consistency.
Stir in the cream and bring the sauce to a gentle boil. Reduce heat to low and gradually fold in the Parmesan cheese until melted and well combined.
Return the seared chicken and any accumulated juices to the skillet. Spoon sauce over the chicken. Partially cover and let simmer for 5 minutes to reheat and meld flavors.
Garnish with freshly chopped parsley if desired. Serve hot with mashed potatoes and roasted green beans.