Make the vegan cheese: Place the Yukon Gold potatoes and sweet potatoes in a saucepan and cover with cold water by 1 inch. Add a few pinches of salt. Bring to a boil, then reduce the heat and simmer, uncovered, until fork-tender, 8 to 12 minutes.

Drain the potatoes and transfer to a high-speed blender with the garlic, cashews, apple cider vinegar, nutritional yeast, onion powder, salt, olive oil, and water. Blend until smooth.

Make the mac and cheese: Bring a large pot of salted water to a boil. Prepare the pasta according to the package instructions, cooking until al dente. Reserve 1/2 cup of the pasta cooking water before draining.

Drain and transfer the pasta back to the pot. Stir in the vegan cheese sauce, adding up to 1/2 cup pasta water to loosen the sauce, as necessary. Season to taste and serve.