Place basil leaves and pine nuts into a food processor.
Add chunks of parmesan and garlic to the processor.
Blend until the basil and cheese are finely chopped.
Pour in olive oil in a thin stream while the motor is running.
Ensure the pesto is thick enough to drop off a spatula.
Transfer the pesto to a bowl and cover until needed.
Boil a large pan of salted water and add the pasta.
Add potatoes and carrots to the pan after 8 minutes of boiling.
Boil for 2 minutes then add the green beans for 3 more minutes.
Drain the pasta and vegetables when the pasta is al dente.
Toss the drained pasta and vegetables with the pesto.
Serve with extra cheese and a sprig of basil.