Place a large pot of water with 1 teaspoon of salt to boil over the stove at medium-high heat. Meanwhile, prepare the pesto sauce.
In a high-speed blender, add cashews, water, extra-virgin olive oil, fresh basil, fresh mint, nutritional yeast flakes, lemon juice, garlic, and salt. Process until pesto sauce is at your desired texture. Set aside.
Add pasta to boiling water, and cook the pasta according to the package directions. While the pasta is boiling, cut your tomatoes in halves. Drain pasta using a colander, and rinse with cold water. Transfer pasta to a large bowl.
Mix pasta with pesto, and stir to coat pasta. Sprinkle vegan parmesan on top, and add tomatoes and basil to garnish. Serve immediately, or this pesto pasta can be stored in a covered container in the refrigerator for 3 days.