Bring a large pot of salted water to boil for the pasta. Cook according to package directions. If using broccoli, stir it into the pot when just 2 to 3 more minutes remain. Drain, and transfer the contents to a large serving bowl.
Meanwhile, in a medium-to-large saucepan, warm the oil over medium heat. Add the onion and a pinch of salt and cook, stirring often, until the onion is tender and turning translucent, about 5 minutes.
Add the grated potato, garlic, garlic powder, onion powder, mustard powder, salt and red pepper flakes. Stir to combine, and cook, stirring constantly, for about 1 minute to enhance their flavors.
Add the cashews and water, and stir to combine. Let the mixture come to a simmer. Continue simmering, stirring frequently and reducing heat as necessary to avoid a rapid boil, until the potatoes are completely tender and cooked through, about 5 to 8 minutes.
Carefully pour the mixture into a blender. Add the nutritional yeast and 2 teaspoons vinegar. Blend until the mixture is completely smooth, about 2 minutes, stopping to scrape down the sides if necessary. If the mixture won’t blend easily or if you would prefer a thinner consistency, add water in ¼ cup increments, blending after each one.
Taste, and blend in additional salt until the sauce is utterly irresistible (I typically add at least another ½ teaspoon). If it needs a little more zip, add the remaining teaspoon of vinegar. Blend again.
Pour the sauce into the bowl of pasta. Stir until well combined, and serve immediately. Leftovers keep well, chilled and covered, for 3 to 4 days. Gentle reheat, adding a tiny splash of water if necessary to loosen up the sauce.