Put basil, spinach, walnut, garlic, olive oil, 1/8 teaspoon of salt and pepper into a food chopper. Process into a coarse mixture.
Place all-purpose flour, egg and breadcrumbs into individual shallow bowls/plates. Beat the egg.
Place chicken breasts on a cutting board and place a piece of plastic wrap over them, slightly pound to even thickness.
Using a sharp utility or paring knife, make a deep pocket inside the chicken breasts. Don't cut all the way through.
Divide the stuffing into two equal parts and put each part into each breast. Gently press to slightly flatten. Season the outside of the chicken breast with salt and pepper.
Dust the chicken breasts with all-purpose flour. Dip into the egg, and then coat with breadcrumbs.
Heat at least 1/2 inch of oil in a frying pan. When the oil reaches 350F, place the chicken breasts into the pan. Fry at moderate heat from 4 to 5 minutes each side, or until the internal temperature reaches 165F.
Transfer to a plate lined with paper towel or cooling rack to absorb/drain excess oil. Move to serving plate, squeeze some lemon juice over it and enjoy.