Heat a small pan over medium heat. Add walnuts to pan; cook for 4-5 minutes or until lightly toasted, stirring constantly. Remove from pan.
ransfer nuts to a food processor; process until minced. Add basil, oil, salt, and peppers; process until blended, scraping sides occasionally. Add cheese; process until smooth.
Spoon into a bowl; fold in tomato. Serve as you like.