Slice the chicken breasts lengthwise to make 4 thin cutlets, trim off any fat, then season them with salt, pepper, and garlic powder before coating them in flour. The cutlets should look evenly dusted rather than thickly coated, and thin pieces will cook quickly and stay more tender.

Add 2 tablespoons of the butter and the olive oil to a skillet over medium-high heat. When the butter melts and foams with the oil, the pan is ready for searing.

Cook the chicken for about 4 to 5 minutes per side, then move it to a plate once both sides are golden. The crust should be deep golden brown, and an instant-read thermometer should reach 165°F for poultry.

Take the skillet off the heat and add the chicken broth, lemon juice, lemon zest, remaining 2 tablespoons of butter, and capers, scraping up the browned bits from the bottom. The pan will smell intensely lemony and buttery, and those browned bits melt into the sauce for extra flavor.

Stir in the cream, return the skillet to the heat, and once the sauce starts bubbling again, nestle the chicken back into the pan. The sauce may look loose at first, but it will start to come together as it warms and simmers around the chicken.

Cook for another 5 minutes, lowering the heat if the sauce is boiling too hard, until the chicken is cooked through and the sauce has reduced to your liking. The finished sauce should lightly coat a spoon, and a splash of extra broth will loosen it if it reduces too far.

Garnish with freshly chopped parsley and/or parmesan cheese if desired. The fresh garnish adds color and a final hit of flavor right before serving.