Place the Basil, garlic, and salt in a food processor and blend until smooth.
Add in your Pecorino, Parmesan, and Pine Nuts. Blend until smooth.
The amount of olive oil you will add next will depend on the consistency of your pesto. Add in a little olive oil at a time and blend until your pesto reaches the consistency of dense cream. You may not need the whole 1/2 cup of olive oil.
Boil your water for your pasta. Once the water comes to a boil, place your pasta, potato, and green beans in the water and cook according to pasta package directions. When finished cooking, drain.
Place your pesto in the bottom of a serving bowl. Add your pasta, potatoes, and green beans on top of your pesto. Mix until all your pasta is covered in the pesto. Serve immediately.