Use a cheese grater to grate the zucchini. Place a kitchen towel in a bowl and place the zucchini in the towel. Sprinkle with salt and allow to sit for 5 minutes. Squeeze out as much liquid as possible.
Put a pot of water on the stove to boil.
Melt the vegan butter in a skillet over medium heat. Add the zucchini, shallot, and a pinch of salt & pepper. Lower the heat and sauté for 20 minutes, or until the veggies are super jammy.
Meanwhile, add the pasta to the boiling water and cook until al dente.
Add the garlic, lemon zest, lemon juice, cream & pesto to the zucchini. Cook on low until the pasta is done.
Use tongs to transfer the pasta to the zucchini. Pour in 1 cup of pasta water & the parmesan and toss until the pasta is coated and the sauce is formed. Add in the basil and give it one more toss. Taste and adjust the seasonings as needed.
Serve hot with extra basil and more vegan parmesan.