Puree the basil with all the other ingredients up to and including the pepper. Mix in the cheese, gradually stir in the oil.
Season the chicken. Mix the panko breadcrumbs with half of the pesto. Spread the pesto mixture on top of the chicken, roll up and secure with toothpicks.
Heat the oil in a non-stick frying pan. Fry the rolls on all sides for approx. 10 mins. Serve with the remainder of the pesto.