Remove basil leaves from stems and wash basil well, spin in salad spinner to dry.
Whirl the basil, garlic, nuts and Parmesan in a food processor until well mixed. Then add the olive oil in a slow, steady stream until a smooth paste is formed.
This will keep in a tightly closed jar in the refrigerator for a week. To freeze, put two tablespoons (one serving) in a muffin cup or on a cookie sheet and freeze until solid and then put in plastic bag.
Put pesto on a serving of hot pasta and top with chopped tomatoes and extra Parmesan. Try it spread on a slice of bread or on a pita with lettuce and tomatoes.