Step 1: Butterfly the chicken breasts by slicing horizontally through the middle and then pounding them to an even 1/4-inch thickness using a meat mallet.
Step 2: Mix the flour, salt, and pepper in a shallow bowl. Dredge the chicken pieces through the flour, shaking off any excess.
Step 3: Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Sear the chicken for 3 minutes per side until golden brown.
Step 4: Remove the chicken from the skillet and set aside on a plate.
Step 5: Add the white wine to the hot skillet, scraping the bottom to release the fond. Let it reduce by half.
Step 6: Stir in the chicken stock, lemon juice, and capers. Simmer for 3 minutes until slightly thickened.
Step 7: Turn off the heat and whisk in the remaining 2 tablespoons of cold butter until the sauce is glossy and emulsified.
Step 8: Return the chicken to the pan to coat with sauce, sprinkle with parsley, and serve.