Holding your knife parallel to the cutting board, cut chicken breasts in half to make thinner fillets. Working with 1 piece of chicken at a time, place inside a gallon zip-top bag and seal the bag, pressing out as much air as possible. Pound with the flat side of a meat mallet, rolling pin, or small skillet to an even 1/4-inch thickness.
In a shallow plate, place 1/2 cup all-purpose and add 1/2 tbls of kosher salt and 1 tsp of black pepper. Dredge chicken one piece at a time in the flour until evenly coated, shake gently remove any excess flour. Place on a large plate or cutting board and repeat with the remaining chicken, placing them in a single layer.
Heat 2 tablespoons of the olive oil in a large skillet over medium heat until shimmering. Cook chicken in batches so that you don't crowd the pan. Cook for 4 minutes each side and remove to a clean platter. Add olive oil if the pan is dry, and repeat with the remaining chicken removing to platter after cooking.
Add 1/2 cup dry white wine to the pan to deglaze and cook until reduced by half. Add the lemon juice, 1 cup low-sodium chicken broth, and 1/2 teaspoon kosher salt to taste. Simmer for 4 to 5 minutes. Add 2 tablespoons unsalted butter and stir until melted. Add chicken to pan, turn off heat, and sprinkle with parsley.
Plate and enjoy!