To begin, you want to start your pesto sauce by toasting the raw walnuts in the oven at 350°F for 10 minutes or until golden brown. This step is not an absolute must, but the pesto will come out much better if you take the few extra minutes to do this.
Once the walnuts are done toasting, start bringing a large pot of salted water to a boil to cook the pasta.
Next, add all the remaining pesto ingredients into the bowl of your food processor along with your toasted walnuts EXCEPT FOR THE OLIVE OIL and WATER. Then pulse until well chopped and mixed.
Now, as the food processor is running slowly add in the olive oil in a stream. It’s important not to add the oil too quickly at this stage. Then continue running the food processor until the pesto is well combined and smooth. If the pesto is still a tad too thick after you have added the oil, you can add about a tablespoon of water to thin it out.
Prepare the pasta according to the package directions in your salted boiling water.
While the pasta is cooking cut the bigger tomatoes in half if need be. You want them to be bite size.
Drain the pasta once done and then put back into the pot. Now, mix in the pesto sauce. At this point if it seems too dry to your liking you can add more olive oil or a touch of warm water.
Then add in the tomatoes and give it a toss.
Taste and season to your liking with salt and fresh ground pepper. But keep in mind that if you are planning to garnish with the vegan parmesan cheese that will add a touch of salt.
To complete the dish, top with more fresh arugula, vegan parmesan cheese, and lemon wedges if desired.
This dish can be eaten hot or cold.