Slice chicken breasts in half lengthwise, then season on both sides with salt and pepper.
Dredge the chicken in flour.
Heat a large skillet over medium-high heat. Add butter and oil. Once heated, add the chicken and sear on each side for 3-4 minutes until golden brown. Remove from heat.
Note: You don't want to crowd the pan so you may need to do this in batches. If so, add the same amount of butter and oil for each batch.
Using the same pan, saute minced garlic for 2-3 minutes until fragrant.
Next, mix in the rest of the butter, chicken broth, white wine, lemon juice, zest and capers. Use a wooden spoon to mix well and scrape up any brown bits that stick to the bottom of the pan.
Return the chicken to the pan and simmer, uncovered, over low heat for about 10-15 minutes. The sauce should be reduced to the desired consistency and the chicken should be at an internal temperature of 165°. Stir the sauce occasionally and turn chicken over halfway through cooking.
Garnish with lemon slices and chopped parsley. For extra flavor, spoon the extra sauce over the chicken before serving. Enjoy!