Slice each chicken breast in half crosswise to make 4 cutlets. Lightly pound each cutlet between sheets of plastic wrap to an even thickness.
Season each chicken cutlet with salt and pepper on both sides. Spread the flour on a plate, and dredge each cutlet in flour. Shake off any excess flour and transfer to a plate.
In a large skillet, heat 3 tablespoons of olive oil over medium-high heat. Working in batches, if necessary to avoid crowding the pan, cook the chicken cutlets for about 3 minutes per side or until golden brown. Remove the chicken from the skillet and transfer them to a plate.
Remove the skillet from the heat and add 2 tablespoons of butter. When the butter is melted, stir in the garlic.
Return the skillet to the heat and cook the garlic for about 30 – 50 seconds, stirring constantly to prevent the garlic from burning. Add the wine and bring to a boil, scraping up any browned bits stuck to the bottom of the skillet.
Pour in the broth, lemon juice and capers and stir to combine. Lower the heat and add the remaining butter. Using a whisk, stir in the butter vigorously to form a sauce. Simmer for about 2 minutes and check for seasoning.
Return the chicken (and any collected juices) to the skillet and simmer until the chicken is completely cooked through, about 3-4 minutes (time will vary depending on the thickness of each chicken breast cutlet).
Stir in the parsley and serve with lemon slices if desire.