Pour hot water over the cashews and let them soak for at least 5 minutes to soften—this will ensure your sauce blends into a silky, creamy texture. While they soak, bring a large pot of salted water to a boil for the pasta. I find soaking cashews in hot water is much faster than cold soaking and gives you better control over the cooking timeline.
Add the spaghetti to the boiling water and cook according to package directions until al dente. Reserve 1/2 cup of pasta cooking water before draining—this starchy water will help adjust the sauce consistency later. Drain the pasta and set aside.
Heat the olive oil in a large skillet over medium heat and add the minced garlic, cooking for about 1 minute until fragrant but not browned. Add the spinach in batches, stirring frequently until completely wilted and any excess moisture has evaporated—this concentrates the spinach flavor and prevents a watery sauce. This should take about 3-4 minutes total.
Transfer the sautéed spinach and garlic to a blender along with the drained cashews, nutritional yeast, salt, lemon juice, lemon zest, and vegetable broth. Blend until completely smooth and creamy, about 1-2 minutes. I like to stop and scrape down the sides halfway through blending to ensure everything incorporates evenly. If the sauce seems too thick, add a splash of the reserved pasta water to reach your desired consistency.
Pour the green sauce into the skillet you used for the spinach and garlic, or into the pasta pot. Add the cooked pasta and toss thoroughly to coat every strand, adding reserved pasta water a tablespoon at a time if needed to reach a silky, flowing consistency. Heat through over medium for about 1-2 minutes, stirring gently.
Divide the green pasta among serving bowls and serve immediately while hot. Add any desired toppings such as additional lemon zest, toasted breadcrumbs, or fresh herbs.