Place the chicken breasts side by side on a cutting board and lay a piece of plastic wrap over them.
Pound the chicken breasts with a studded meat mallet, until they are about 1/4-inch thick.
Place some flour in a shallow platter and season it with a fair amount of salt and pepper; mix with a fork to distribute evenly.
In a wide bowl, beat the eggs and set aside.
Meanwhile, heat olive oil over medium-high heat in a large skillet.
Dredge both sides of the chicken cutlets in the seasoned flour, and then dip them in the egg wash to coat completely, letting the excess drip off.
When the oil is nice and hot, add the cutlets and fry on each side until golden, turning once (about two minutes per side).
Remove the chicken cutlets to a large platter and lay in a single layer to keep warm.
In the same pan that you cooked the chicken, add the wine, broth, capers, and lemon juice. Simmer for 5 minutes to reduce the sauce slightly.
Roll the butter in some flour and add it to the skillet (this will thicken the sauce). Stir to incorporate and dissolve the flour.
Reduce the heat to medium-low and return the chicken to the pan.
Simmer gently for about two minutes to heat the chicken through (165 degrees internal temperature). Season with salt and pepper and garnish with chopped parsley before serving.