Butterfly the chicken breasts lengthwise into two cutlets. Cover with plastic wrap or parchment and pound to a 1/4 to 1/2" thickness with a meat mallet or rolling pin.

In a large mixing bowl or a large ziplock bag, place flour, salt and pepper. Add in the chicken and toss until dusted. Shake off the excess flour.

In a large skillet over medium-high heat add 1 T of olive oil and 1 T of butter. When it starts to foam and the foam subsides, add half of the dredged chicken in a single layer. Cook about two minutes, until light golden brown, then flip and cook the other side. Transfer the cooked chicken to a plate and return the pan to the stove. Add another tablespoon of olive oil and butter, let it brown and when the foam subsides add the remainder of the chicken. Transfer to plate when done.

Return the skillet to stove and add the final tablespoon of olive oil and butter along with the minced shallot or garlic. Saute until it begins to color, about 1 minute, then pour in the white wine. Scrape with a spoon to release the brown bits in the skillet and boil until the wine has nearly cooked away, then stir in the chicken broth. Continue cooking until the broth has reduced by about half.

Stir in the lemon juice and capers, then add the chicken, tossing to coat which will also thicken the sauce. Check for seasoning, adding more salt and pepper as necessary. Simmer for about a minute to heat the chicken through.

Garnish with chopped Italian parsley and more lemons.