Bring a large pot of generously salted water to a boil. Cook the pasta two minutes shy of the package directions — it will finish cooking in the sauce.
Grate and salt: Grate the zucchini using the large holes of a box grater or the grating disc of a food processor. Toss the shreds with 1 teaspoon of salt directly in a colander. Let it sit over the sink or a bowl for 10 minutes. You'll see green-tinted water pooling — that's exactly what you want.
Squeeze: Transfer the zucchini to a clean kitchen towel. Gather the corners and twist tightly over the sink. Really twist. You'll be shocked at how much water comes out — sometimes up to a cup.
Sauté: Heat the olive oil or butter in a large skillet over medium heat. Add the squeezed zucchini and minced garlic. Cook, stirring frequently, for 4-5 minutes. It should smell sweet and vegetal, not wet or steamed.
Blend (optional): Transfer the cooked zucchini mixture to a blender or use an immersion blender. Pulse until smooth. For a chunkier sauce, leave as is.
Make it creamy: Return the zucchini to the skillet (or keep it there if you skipped blending). Reduce heat to low. Stir in the heavy cream or coconut milk, the Parmesan or nutritional yeast, and the lemon zest. Stir for about 1 minute until combined and warm.
Add the pasta water: Ladle in the reserved pasta water, a splash at a time, stirring constantly. The sauce should loosen and become glossy — it should coat the back of a spoon.
Toss the pasta: Add the drained pasta (undercooked by two minutes) directly to the sauce. Toss vigorously for 1-2 minutes over low heat. The sound should shift from a liquid splash to a soft, slick coat. Add another splash of pasta water if it looks dry.
Finish and serve: Taste and adjust salt if needed. Top with fresh basil, red pepper flakes, and extra Parmesan. Serve immediately.