Cook a large pot of salted water to a rolling boil, then add your vegan pasta. Cook until al dente, about 8-10 minutes, then drain, saving a little pasta water for adjusting sauce consistency.
While the pasta cooks, drain the soaked cashews and add them to a high-speed blender along with nutritional yeast, mustard, lemon juice, smoked paprika, and plant-based milk. Blend until completely smooth and creamy, about 1-2 minutes, stopping to scrape down the sides if needed.
Pour the blended sauce into a saucepan and warm over medium heat. Stir constantly and cook for 3-5 minutes until it thickens slightly and becomes fragrant, with a glossy, velvety texture.
If the sauce becomes too thick, add a splash of reserved pasta water and stir until smooth and pourable.
Taste the sauce and adjust seasonings as needed—adding more lemon juice for brightness or more nutritional yeast for cheesiness.
Add the cooked pasta to the sauce, tossing gently to coat each piece evenly. Continue to cook together for 1-2 minutes until warmed through and the sauce clings to the pasta.
Transfer the cheesy pasta to a serving bowl, and let it sit for a minute or two for the flavors to meld. Serve hot, garnished with fresh herbs if desired.
