Place the pasta and water in a 10-ounce microwave-safe mug. Microwave for 1 1/2 to 2 minutes, stirring a few times toward the end to prevent the water from boiling over.
Stir in the milk, pumpkin puree, and kosher or sea salt, then microwave 1–2 minutes more, stopping to stir occasionally. Cover and let rest for 3–5 minutes, then check that the pasta is cooked through.
Stir in the shredded cheese, cover, and microwave 1 minute until the cheese is melted.