Season chicken with salt and pepper, then coat with mixture of almond flour and arrowroot. Shake off excess.
Melt 2 tablespoons ghee or butter with 3 tablespoons olive oil in large skillet over medium-high heat. When liquid starts to sizzle, add both pieces of chicken. Cook until chicken is browned, about 2 1/2 minutes. Flip and cook other side additional 2 1/2 minutes. Remove chicken and transfer to plate.
Add garlic to skillet and stir several times, then add the lemon juice, chicken stock, and capers. Bring to a boil, stirring occasionally to mix any seasoning that may be at bottom of skillet. Simmer for 5 minutes.
Add chicken breasts to lemon mixture. Flip to coat. Cook about 30 seconds. Remove chicken and serve over the starch of your choice. Garnish with parsley.
For Whole30: Use ghee instead of butter and serve over zoodles, mashed potatoes, or cauliflower rice.
For Paleo: Use ghee instead of butter and serve over heart of palm noodles, shirataki noodles, or zoodles.
For gluten-free: Serve over gluten-free pasta.
Butterflying a chicken breast: Place your hand on top of a boneless, skinless chicken breast. Slice horizontally into the breast, dividing it half, cutting until about a half inch from the opposite side. When you're done, you should be able to open the chicken breast like a book.