Preheat the oven to 200 degrees F. Line a small baking sheet with paper towels. If using full chicken breasts, lay them on a cutting board and cut each breast in half, parallel to the cutting board, to create 4 thin pieces.
Place a large skillet on the stovetop and set to medium-high heat. Set a shallow pan next to the stove and pour the almond flour in it. Add 1/2 teaspoon salt and 1/4 teaspoon ground black pepper. Mix well.
Add 3 tablespoons oil to the skillet. Once hot, dip the four chicken cutlets in the almond flour, coating well on both sides. Then gently place them in the hot oil.
Fry the chicken for 3 minutes per side. Use tongs to move them onto the prepared baking sheet and place them in the oven to keep warm.
Pour the oil out of the skillet and wipe the dark crumbs out with a paper towel. Then set the skillet back over medium heat. Add the butter (or 3 more tablespoons oil) to the skillet and whisk in the arrowroot powder, chicken broth, white wine, and lemon juice.
Bring to a simmer. Once the sauce is thick enough to coat a spoon, add in the capers. Stir well.
Place the chicken back in the skillet. Flip the chicken to coat it in the lemon sauce. Then serve with a generous sprinkling of parsley. Serve immediately.
Paleo? Use 6 tablespoons olive oil instead of butter. Keto? You can substitute more broth for the wine to lower the carbs.