Prep the chicken: Halve and juice one of the lemons, reserving the other half for thin slices. Set aside. Place the flour in a shallow bowl. Pound the chicken breasts to an even thickness between sheets of plastic wrap using the flat side of a mallet or rolling pin. Season the chicken with salt and pepper, then dredge in flour, shaking off the excess. See tips below.
Cook the chicken: Heat 2 tablespoons of olive oil and 3 tablespoons of butter in a large skillet over medium-high heat. Add the chicken and cook in batches until golden, about 4 minutes per side. Transfer to a plate and keep warm.
Make the sauce: Lower the heat to medium and add the remaining 2 tablespoons of olive oil to the skillet. Add the sliced garlic and chopped capers, cooking for 1-2 minutes until fragrant.
Simmer and reduce: Pour in the white wine, scraping up any browned bits from the bottom of the pan. Simmer for about 5 minutes until the wine reduces by half. Add the chicken broth, remaining 3 tablespoons of butter, 1 teaspoon of salt, and a good grind of pepper. Stir until the butter melts.
Finish the dish: Stir in the lemon juice, then return the chicken to the pan and let it simmer for 3 minutes, or until the chicken is fully cooked and heated through. Add the reserved lemon slices and cook for an additional minute. Remove from heat, garnish with chopped parsley, and serve. Enjoy!
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