01 - Butterfly each chicken breast by slicing horizontally through the center, then gently pound between plastic wrap to 1/2-inch thickness. Season both sides generously with salt and pepper.
02 - Lightly coat each chicken breast in flour, shaking off any excess coating.
03 - Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Add chicken and cook 3 to 4 minutes per side until golden brown and cooked through. Transfer to a plate and cover loosely with foil.
04 - Pour white wine into the skillet, scraping up any browned bits from the bottom. Simmer for 1 to 2 minutes until slightly reduced.
05 - Add chicken broth, lemon juice, and capers to the pan. Simmer for 2 to 3 minutes until the sauce reduces by approximately one-third.
06 - Return chicken to the skillet and simmer 2 minutes, basting with the sauce. Remove from heat and stir in remaining 1 tablespoon butter along with half the parsley until sauce becomes glossy.
07 - Arrange chicken on serving plates, spoon sauce generously over each portion, and garnish with lemon slices and remaining parsley.