Slice chicken breasts in half crosswise into 4 cutlets and lightly pound each piece between sheets of plastic wrap until an even thickness (about ½" thick or less).
In a medium bowl, beat the eggs with ½ teaspoon salt. Toss the almond flour with ½ teaspoon salt and ¼ teaspoon pepper and spread the mixture on a large plate. Dip each chicken cutlet in the egg, letting any excess drip back into the bowl, then coat the chicken with the almond flour.
In a large heavy skillet, heat the oil over medium high heat. Add the chicken and brown it, turning once, 5 to 6 minutes total. Transfer the chicken to a plate. Working in batches if needed to avoid overcrowding the pan. Chicken will be nearly cook through.
Add the garlic to the skillet and cook, stirring, until golden, 2 to 3 minutes. Stir in the wine, stock, capers, lemon juice and zest. Bring the sauce to a boil and then simmer until the sauce is reduced by half. Whisk in the butter until combined, then return the chicken to the skillet and let it gently cook through, about 2 minutes. Sprinkle the chicken with the parsley and serve.
If you cook the chicken in batches, I recommend wiping out the pan and adding additional olive oil to prevent the almond flour from burning.
Leftover chicken can be stored covered in the fridge for 2 to 3 days. Reheat on the stove top or in the microwave.