Bring a large pot of salted water to a boil. Add carrots; cover partially and simmer for 5 minutes. Add parsnips; cover partially and simmer until vegetables are very tender, about 15 minutes. Drain well. Return vegetables to the pot and stir over medium heat until any excess moisture evaporates.

Transfer vegetables to a food processor. Add butter; process until smooth. Season with nutmeg, salt, and pepper.