Add edamame to the food processor along with the spinach, basil, cashew milk, lemon juice, salt and pepper. Pulse until it starts to get smooth, scrape sides if spinach is sticking. Blend until finely chopped and smooth. Add lemon juice, salt and pepper if needed.
Boil water with olive oil and salt and cook until al dente. Drain and set aside.
While the pasta is boiling, place olive oil in a skillet and cook down the shallots. When they start to soften add in the roasted garlic, toss a few times.
Add in the cooked spaghetti, pasta water and pesto and give a few big tosses and let heat for a few minutes until it thickens a bit.
Top with vegan parmesan and a few basil leaves. Serve right away while warm.