Pour beaten egg into shallow bowl. Set aside.
Add almond flour, coconut flour, tapioca starch, salt, and garlic powder to second shallow bowl or food-safe sealable bag. Whisk or shake until dry ingredients are well blended. Set aside.
Line plate with paper towels. For crispier chicken, place wire cooling rack over paper towels. Set aside.
Lay chicken breasts in shallow bowl with beaten egg. Cover all sides of chicken with egg and let any excess drip back into bowl, then transfer chicken to bowl or bag with "breading" mixture. Repeat with remaining chicken breast. Coat chicken with "breading" pressing gently to make sure dry ingredients stick well. If using food-safe bag, seal bag and shake until chicken breasts are well coated in dry mixture. Set aside.
Heat large cast iron skillet over medium heat. When skillet is warm, add thin layer of refined coconut oil or avocado oil and continue warming until oil is hot and shimmery.
When oil is hot, place chicken breasts in skillet. Fry chicken 3 minutes, then flip chicken over and fry 3 to 4 minutes more, until "breading" is golden brown and chicken is cooked through. Note: if chicken is not cooked through after 7 minutes total, reduce heat under skillet to low and cover skillet with lid. Cook chicken 2 minutes covered, then check doneness again. Repeat until cooked through.
When chicken is cooked through, use slotted spoon or tongs to transfer chicken from skillet to plate or wire cooling rack. Let excess oil drip onto paper towels while assembling salad.
Divide lettuce evenly between salad bowls. Top each bed of lettuce with equal amounts of hard-boiled eggs, tomatoes, pecans, and red onion. Slice chicken breasts crosswise into strips and divide between salads, then drizzle ranch dressing over and serve.