In a large pot, add enough water to cover the celery roots and potatoes by 1 inch. Bring to a boil; salt the water and reduce heat to medium. Simmer until tender, about 20 minutes; drain.
Working in batches in a food processor, puree the vegetables; return to the pot. Mash in the milk and 1 stick butter; season with salt and pepper. Transfer to a large bowl. Swirl the top; drizzle with the melted butter and top with pepper.
This recipe is part of our 2-hour holiday dinner menu. Get the rest of the recipes here.