Heat a 13-inch nonstick skillet over medium heat. Add the oil. Add the mushrooms in batches and cook, stirring occasionally until golden brown before adding more mushrooms, 10 to 12 minutes total. Reduce the heat to medium-low and add the garlic, 1 1/2 teaspoons salt, 1/2 teaspoon black pepper and the crushed red pepper flakes. Stir together.
Add the coconut milk, water and nutritional yeast to the skillet. Stir together and taste for seasoning and add more salt or black pepper, if needed. Add the pasta and zucchini and stir, making sure the pasta is submerged in the liquid.
Cover with the lid and simmer for 12 minutes, stirring every 3 to 4 minutes. Uncover and add the basil. Stir and simmer uncovered until the sauce has thickened and the pasta is al dente, 5 to 6 minutes.
Scoop into small shallow bowls and top with more basil and black pepper.