In a small food processor, combine the almond flour and parmesan cheese. Pulse several times until the parmesan is well incorporated into the mixture. Pour the “breading” onto a plate and set aside for now.
Once the chicken breast has been thinly sliced into cutlets, season it with the salt and pepper.
Heat 2 tablespoons of the butter and 1/2 tablespoon of the oil in a sauté pan over medium heat. Dredge the chicken in the almond flour parmesan breading on both sides, then place it in the pan with the oil, working in batches of two pieces of chicken at a time. Cook for about 3 to 4 minutes per side, depending on thickness. Before starting the second batch, add an extra 1 tablespoon of butter and 1/2 tablespoon of oil.
When the chicken is done, set it aside on a plate for now, and prepare your sauce. Add the lemon juice, chicken broth, and capers to the pan. Simmer over medium heat for about 4 to 5 minutes, until the sauce has reduced a little (as a heads up, it will stay thin though). Stir in the remaining 2 tablespoons of butter.
Add the chicken back to the pan just to reheat for a minute or so. Serve the chicken topped with additional sauce. Enjoy!