This version uses both olive oil and butter. Butter is much more widely used in northern Italian dishes than in southern ones, and pesto is originally from Genoa (Genova) in the North West of Italy.
This article gives more history http://www.theatlantic.com/past/docs/issues/98aug/pesto.htm
Step 1: Ingredients
1 cup/ 2 oz / 50g fresh basil leaves
1/2 cup / 4 fl oz / 110 ml olive oil
1/3 cup / 3 oz / 75g pine nuts
2 cloves of garlic
pinch of salt
1 1/2 cups / 4 oz / 100g / freshly grated parmesan (or a mixture of parmesan & pecorino)
1 stick / 2 oz / 50g butter
This makes enough pesto to serve with 1 1/2 lbs / 24 oz / 750g pasta
Step 2: Prepare the Ingredients
Strip the basil leaves from the stalks and discard the stalks
Grate the parmesan
Allow the butter to soften or soften in the microwave
Peel the cloves of garlic
If freezing the sauce it is recommended that you do so before adding the dairy ingredients, though I have often frozen it with the butter and the cheese with no apparent loss of flavour or texture, and even if some is lost it is still much superior to the "pesto" you can buy in jars!
Empty the paste into a bowl and stir in the grated cheese and softened butter.
That's it, your pesto is now made!
Step 4: How to Serve
Cook the pasta until 'al dente' - still slightly firm to the bite, not crunchy, not soggy.
Take 6 to 8 tablespoons of the hot cooking water and stir it into the pesto sauce. Drain the pasta, return to the pan and then stir in the pesto until the pasta is well coated.
Serve immediately with crusty bread and a simple salad.