Place each chicken cutlet between two pieces of plastic wrap and pound to an even ¼-inch thickness. Season both sides generously with salt and pepper.

Place the flour in a shallow dish. Press each chicken cutlet into the flour to coat both sides, shaking off any excess.

In a large skillet, heat the olive oil and 2 tablespoons of butter over medium-high heat. Cook the chicken in batches for 2-3 minutes per side, until golden brown and cooked through. Remove to a plate.

Reduce heat to medium. Add the white wine to the skillet to deglaze, scraping up any browned bits. Simmer for 30 seconds. Add the chicken broth and lemon juice. Simmer for 3-4 minutes to reduce slightly.

Stir in the remaining 3 tablespoons of butter and the drained capers until the butter is melted. Return the chicken to the pan, spooning the sauce over the top to warm through. Garnish with fresh parsley and serve immediately.