Bring a pot of salted water to a boil, and cook your pasta until al dente, following package directions. Reserve 1/2 cup of the cooking liquid, and then drain the pasta without rinsing it.
Make the vegan edamame pesto:
Add the edamame to your food processor and pulse a few times until broken up fairly small.
Add the spinach, basil, nondairy milk, lemon juice, salt, and pepper, and continue to pulse, stopping to stir and scrape the sides if needed, until the spinach and basil are finely chopped.
Add more lemon juice, salt and pepper to taste if desired, and set aside.
Finish the edamame pesto pasta:
In a large pan, heat olive oil over medium heat and add the shallot. Continue to cook, stirring occasionally, until the onion is softened and browning slightly. (Note: to save time, you could begin this step while the pasta is still cooking).
Add the garlic and cook for just about 60 seconds more, stirring occasionally, until the garlic is fragrant.
Add the cooked pasta, reserved pasta water, and pesto and fold everything together gently (I use a silicone spatula for this part). Reduce the heat to medium-low and cook, stirring frequently, until the sauce has thickened slightly and clings to the pasta, and is warm throughout. Remove from the heat and adjust seasoning to taste. Serve warm. The pasta is best eaten immediately; otherwise, fold in a light drizzle of olive oil before storing leftovers and keep in the fridge for up to 3 days.