Add all the pesto ingredients, except the oil, to a food processor and pulse until the ingredients are blended into tiny pieces.
With the food processor running on low, slowly stream in the oil so it emulsifies with the mixture. Stop and scrape down the sides as necessary.
Assemble the salad:
Cook the pasta according to package instructions. (It's best to cook it al dente to prevent the pasta from getting mushy in the salad). Drain, rinse with cold water and drain again.
In a large bowl, add the pasta, tomatoes, peppers, cheese and pesto. Toss to combine and serve.
Notes
Rinse the pasta with cold water to cool it down and remove starch so it doesn't clump together.
Use good quality extra virgin olive oil to avoid a bitter tasting pesto.
It might seem like a lot of pesto for the salad, but some of it will absorb into the pasta, so you'll need it all.
If you prefer to use store-bought pesto, you'll need about ¾ cup for the salad.