Place chicken breasts between sheets of plastic wrap and pound to an even thickness of about 1/4 inch.
Coat chicken with pesto, then dip in flour, then dip in egg mixture and lastly, dip in seasoned bread crumbs combined with Parmesan cheese.
In a large nonstick or well-seasoned skillet, over medium heat, heat 2 tablespoons oil. Add chicken and cook about 2 minutes on, each side, until coating is golden brown and chicken is cooked through. Remove to a baking sheet lined with paper towels. Add more oil to the skillet as needed during frying.