Start by pounding down the chicken: Place chicken as flat as possible in a sealed freezer bag. Make sure there is no air left in the bag! Use a meat tenderizer or the wide base of a jar (we used a peanut butter jar!) and gently pound the chicken until it’s fairly even, about 1/2 inch in depth. Remove chicken from the bag and pat dry with paper towel.
Whisk together dressing ingredients in the bottom of a large bowl. Add the slaw ingredients and toss well. Set aside.
Whisk together dip ingredients. Set aside.
In a shallow dish, mix together almond flour, paprika, garlic powder, onion powder, salt and pepper. In another shallow dish, add eggs.
Heat a cast iron skillet over medium high heat. When skillet is hot, add half of the oil to the pan. While the oil heats up, dip a chicken breast in the egg, coating it fully. Then carefully pat the egg-coated chicken in the almond flour mixture, flipping over and fully coating with the dry mixture. Repeat with each chicken breast.
When oil is shimmering in the pan, add as many chicken breasts to the skillet as you can while keeping them from touching (2 batches usually works well with a 10” skillet) Allow the chicken to cook for about 3 minutes, or until there is a nice golden crust on the bottom of the chicken. Lower the heat to medium low, and flip the chicken, keeping a careful eye on it to keep it from burning, about 6-8 minutes. Remove from the skillet when the chicken is golden on the bottom and cooked through. Wipe the pan well and re-oil between batches.
Allow chicken to rest for 5 minutes before slicing. Serve with slaw and dip.