Shell the pistachios and blanch them in a small pot of boiling water for a minute and a half.
Place the blanched pistachios in a rolled-up, coarse tea or dish towel and use both hands to roll the towel. The husks should easily separate from the nuts.
Place the basil, pistachios, garlic and salt in the mortar. Grind with the pestle by first mashing the ingredients on the bottom of the mortar. After the ingredients are mashed, use a circular motion to grind the ingredients together until they form a paste.
Slowly drizzle in the olive oil and mix with a wooden spoon until incorporated.
Optionally add butter and mix with the wooden spoon until incorporated.
Mix in the Parmigiano-Reggiano and Pecorino Romano until incorporated. Taste the pesto and adjust for salt as necessary.
Notes
You can use a food processor to make this pesto. Grind the basil, garlic, salt and pistachios. Slowly drizzle in the olive oil. Once your paste is formed, move the mixture to a bowl and mix in the parmigiana and pecorino cheeses. Add additional salt as needed.
If you're serving the pesto with pasta, use it immediately. (It's enough for 1 1/2 pounds.) If you're not using it right away, store in a plastic container, placing plastic wrap in direct contact with the pesto to preserve the pesto's color.