Add the olive oil and 2 tablespoons of the butter to a wide pan and heat over medium-high heat.
Using a sharp knife, slice the chicken in half horizontally to create two, thin cutlets.
Lightly sprinkle both sides of the chicken with salt and pepper and dust them with flour, shaking off the excess.
When the oil and butter are hot, add the chicken and cook for 2 to 3 minutes per side, or until lightly browned.
Remove the chicken from the pan and set aside.
Turn the heat down to medium, and add the garlic. Cook for approximately 30 to 60 seconds, stirring constantly.
Add the wine and use a spatula to scrape up all of the bits that are on the bottom of the pan. Simmer for two minutes.
Add the capers, broth and remaining butter to the pan and stir to combine.
Return the chicken to the pan and simmer for three to four minutes.
Turn the heat off and squeeze the juice of two lemons all around the pan. Stir to combine.
Taste the sauce and adjust the salt and pepper to your liking.
Sprinkle in the parsley just before serving.
To serve, arrange the chicken on a platter and pour all of the pan sauce over the chicken.
Thinly slice the remaining lemon and top each piece of chicken with a slice of lemon.
Sprinkle the entire platter with finely sliced basil and a few shavings of fresh Parmesan.