Butterfly the chicken: Slice each chicken breast horizontally so you’re left with thinner, even pieces. If your pieces are still thick, place them between sheets of parchment paper and gently pound them with a meat mallet.
Season and coat: Sprinkle both sides with salt and pepper. Lightly dredge each piece in flour, shaking off excess.
Heat a large skillet over medium-high heat. Add about 1 tablespoon each of olive oil and butter. Place the chicken in the skillet in a single layer. Don’t overcrowd—cook in batches if needed. Sear for 2 minutes on each side until golden brown. Add more oil and butter as necessary. Remove chicken and set aside.
Turn the heat down to medium. Add a splash of olive oil. Toss in shallots, garlic, and capers. Sauté for about a minute, stirring frequently. Pour in white wine to deglaze the pan—scrape those golden bits loose with a wooden spoon. Add the chicken base, lemon juice, and 2 tablespoons of butter. Let the sauce simmer for 2–3 minutes, letting it reduce slightly.
Return the chicken to the pan and nestle it into the sauce. Let everything simmer together for another 2 minutes to heat through. Spoon the sauce over the top of the chicken. Garnish with chopped parsley and fresh lemon slices. Turn off the heat and serve immediately.
