Place the chicken breasts in a plastic bag or between 2 pieces of parchment paper. Pound them to 1 cm ( ¾ inch) thickness. Cut each breast into 2 pieces and season with salt and pepper to taste.
Whisk together the almond flour and 2 tbsp tapioca flour in a shallow bowl. Heat a large skillet over medium heat. Add 2 tbsp of ghee to the skillet.
Working with one piece at a time, dredge the chicken into the flour mixture and shake off the excess. Place in the skillet and cook for 3-4 minutes on each side. You can cook 3 pieces at a time to prevent the skillet from cooling.
The outside of the chicken should be golden when done. Repeat with all the remaining chicken. Transfer them to a plate.
Drop the heat to medium-low and add the remaining ghee to the skillet. Finely chop the onions, mince the garlic, and add them to the skillet. Cook for 1-2 minutes until soft and fragrant.
Add the chicken broth, lemon juice, mustard, and remaining tapioca flour and mix to incorporate. Raise the heat to medium and bring to a gentle simmer, stirring occasionally. Add the capers and let everything simmer for a minute or 2.
Return the chicken to the pan and heat it in the sauce for a minute on low heat. Taste and adjust seasoning if needed. Take it off the heat and serve it immediately.