Combine basil, olive oil, pine nuts, garlic, lemon zest, lemon juice, salt, and pepper in a blender. Process until well blended. Transfer pesto to a container and store in the refrigerator until needed.
Preheat the oven to 350 degrees F (175 degrees C).
Place cauliflower in a steamer insert inside a saucepan filled with 1 inch of water. Cover saucepan, bring to a boil, and steam cauliflower until tender, 5 to 10 minutes. Transfer cooked cauliflower to the blender; add 2 tablespoons of pesto and blend.
Mix garlic powder, cayenne, salt, and pepper together in a small bowl. Place chicken on a work surface and rub spice mixture equally into breasts.
Make a deep cut in the side of each breast to create an opening for stuffing. Heat coconut oil in a skillet over medium heat. Fry chicken on both sides until slightly browned, about 5 minutes total.
Return chicken to the work surface and let cool until safe to handle. Spoon pesto-cauliflower mixture into the pocket of each breast and place on a rimmed baking tray.
Bake in the preheated oven until chicken is no longer pink in the center and the juices run clear, about 20 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
