Prepare the cashews: either soak the cashews in water for 2 hours and then drain, or boil them for 10 minutes and then drain and let cool slightly.
Peel and cube the small potato and peel and chop the medium carrot.
Place the cubed potato and chopped carrot in a saucepan and add enough water to cover them. Bring to a gentle boil, then reduce the heat and simmer 10–15 minutes, or until the potato and carrot are fork-tender.
Drain the cooked vegetables and discard the cooking water.
Add the drained vegetables and the prepared cashews to a blender. Add 1 cup water, 1 cup unsweetened plain plant-based milk, 2 teaspoons onion powder, 2 teaspoons garlic powder, 2 teaspoons paprika, the juice of 1 lemon, ½ cup nutritional yeast, 2 tablespoons vegan butter, and 1 teaspoon salt.
Blend on high until completely smooth, stopping to scrape down the sides as needed to get an even, creamy texture.
Transfer the sauce to a saucepan and heat gently over medium-low, stirring, until hot and the butter is fully incorporated (about 3–5 minutes). Taste and adjust seasoning if desired, then serve.