Pound each chicken breast to ¼ inch thick between plastic wrap. Mix the ½ cup flour, ½ tsp salt, and ¼ tsp black pepper in a shallow bowl, dredge the chicken, and shake off the excess.

Heat the 3 tbsp olive oil and 1 tbsp butter in a large skillet over medium-high heat. Sear the chicken for 3 to 4 minutes per side until deep golden and cooked to 165°F (74°C). Transfer to a plate and cover loosely with foil.

Reduce heat to medium, add the 3 cloves minced garlic, and cook for 30 seconds. Pour in the ½ cup white wine, scrape up the browned bits, and simmer for 2 minutes until reduced by half.

Add the ¾ cup chicken stock and 3 tbsp lemon juice. Simmer on medium-high for 3 to 4 minutes until slightly reduced, then stir in the 2 tbsp capers.

Reduce heat to low, stir in the remaining 2 tbsp butter, slide the chicken back in, and spoon sauce over it for 1 minute. Scatter the 2 tbsp chopped parsley on top and serve on a plate with lemon slices alongside.