This was pretty good for my first time out.
2 cups fresh basil leaves, packed
1/2 cup freshly grated Parmesan-Reggiano or Romano cheese
1/2 cup extra virgin olive oil
1/3 cup pine nuts or walnuts
3 medium sized garlic cloves, minced
Salt and freshly ground black pepper to taste
Special equipment needed: A food processor
Combine the basil in with the pine nuts, pulse a few times in a food processor. (If you are using walnuts instead of pine nuts and they are not already chopped, pulse them a few times first, before adding the basil.) Add the garlic and cheese and pulse a few times more.
Slowly add the olive oil in a constant stream while the food processor is on. Stop to scrape down the sides of the food processor with a rubber spatula. Add a pinch of salt and freshly ground black pepper to taste.
Serve with pasta, or over baked potatoes, or spread over toasted baguette slices.
If you're making it with shrimp, like I did, toss those suckers in a frying pan with olive oil, lemon and salt, then toss with the pasta!