Add the diced potato to the water once it has begun to boil.
Prepare for four minutes.
To the boiling water, add the pasta in step 6.
After 8 minutes of pasta and potato cooking, add the cleaned green beans.
Cook for an additional 5-8 minutes or until the pasta is al dente.
Set aside about 1/3 cup of the pasta water before draining it to combine with the pesto sauce.
After straining the pasta, do not rinse it.
Set aside.
Combine one teaspoon of salt, basil, garlic, cheeses, half a cup of olive oil, and pine nuts in a mortar and pestle or food processor. If you have allergies, leave the pine nuts out.
A thick purée or paste should result from the mixing. Add some extra virgin olive oil if your pesto is too thick.
Add two tablespoons of pesto and roughly a third cup of pasta water to a large serving bowl.