In a large measuring cup with a spout, combine the sauce ingredients and set aside. Before you start cooking, measure out the remaining ingredients for convenience.
Slice the chicken breasts in half lengthwise to create 2-3 thinner pieces. Cover the chicken with plastic wrap and, using the textured side of a meat mallet, gently pound it to a thickness of ½ inch.
Season both sides of the chicken with salt, pepper, and parsley.
In a large skillet, heat olive oil over medium-high heat. Sear the chicken in batches for 4-5 minutes on each side, or until a golden crust forms. Once cooked, set the chicken aside.
Turn off the heat briefly, then add the broth to the skillet. Turn the heat back to medium and use a silicone spatula to scrape the bottom and sides of the skillet; this will help incorporate the flavorful “fond” into the sauce. Allow the mixture to come to a gentle bubble and let it reduce for 2 minutes. After that, add minced garlic and cook for an additional 2-3 minutes, until the liquid has reduced by half.
Add the butter and flour to the skillet, stirring to combine them well. Cook for 1-2 minutes to eliminate the raw flour taste.
Gradually add the sauce mixture (prepared in step 1) in small splashes, stirring continuously to ensure a smooth consistency. Bring the mixture to a boil, then reduce the heat to a simmer. Allow it to simmer and reduce for about 8 minutes.
Lower the heat to low and slowly sprinkle in the Parmesan cheese while stirring continuously until melted. Next, stir in the lemon juice for added brightness.
Return the chicken to the skillet and spoon the sauce generously over the top. Heat through for 5 minutes, or until the sauce has reached your desired thickness.