Fill a large saucepan with water and bring to a boil. Once the water is nearly boiling, add a generous amount of salt to the water. Add the linguine and cook according to the package instructions.
Meanwhile, prepare the avocado sauce. In a food processor, add the flesh of the ripe avocados, almond milk, lemon zest, lemon juice, basil leaves, salt, pepper, garlic powder and cayenne. Purée until completely smooth and creamy, scraping down the sides of the food processor with a rubber spatula as needed.
Once pasta is al dente, drain the pasta but reserve 1/2 cup of the cooking liquid. Pour the avocado sauce over the hot pasta and toss to combine. If the sauce is too thick, add some of the reserved pasta water to thin out.
Finish pasta with fresh basil, cherry tomatoes, hemp seeds and cashew parmesan (if using).