Start by slicing each chicken breast lengthwise into two thinner halves. If they’re uneven, use a meat mallet to pound them to uniform thickness. This ensures the chicken cooks evenly.
Season the chicken with salt, pepper, and garlic powder. Then dredge each piece lightly in flour until fully coated. Shake off any excess to avoid a gummy texture.
Heat 2 tablespoons of butter and the olive oil in a large skillet over medium-high heat. Once the butter has melted and starts sizzling, place the chicken pieces in the skillet. Fry for about 3-4 minutes per side until they’re golden and cooked through. Remove from the skillet and set them aside on a plate.
Turn the heat down slightly and add the chicken broth, lemon juice, and lemon zest to the skillet. Use a wooden spoon or spatula to scrape up the browned bits from the bottom of the pan. Simmer for 2-3 minutes.
Stir in the remaining butter and capers. For a creamier version, add the heavy cream at this stage and whisk gently until the sauce thickens slightly. Taste and adjust for salt if needed.
Place the cooked chicken back into the skillet, coating each piece in the sauce. Allow it to heat for another minute or two, then remove from the heat.