Cook the pasta according to the instructions and set aside
Bring a pot of water to a boil, add the carrots and cashews (if using JOI, only add the carrots), and cook for ~10-15 minutes until they’re soft and can easily be pierced with a fork
Drain the carrots and cashews, then transfer to a blender or food processor
Add all of the remaining ingredients to cooked carrots and cashews, and blend until smooth – can add extra liquid if needed to reach the desired cheese sauce consistency
Pour the mixture into a pot over low-medium heat (can reuse the pot used to boil the carrots and cashews), stirring consistently for a few minutes to melt any remaining cheese that wasn't fully blended – be sure to scrape the sides of the pot while stirring so the sauce doesn’t begin to cook and harden around the edges; lower the heat if needed
Remove the cheese sauce from the stove and combine with the cooked pasta. This can be done one of two ways: put ~12 oz. of pasta in a large bowl and mix the sauce in, adding more pasta until the desired consistency and cheesiness is reached or gradually incorporate the pasta directly into the cheese if the pot is large enough to accommodate the pasta