Tangy and aromatic, celeriac (or celery root) has long been a staple in French cooking. Here, it's combined with parsnips and russet potatoes for a side dish worthy of your favorite bistro—or trattoria, because we've relocated the dish south, from Paris to Tuscany, using olive oil and Parmesan cheese. The potato is kept separate from the celeriac and parsnip because it gets gluey when pureed in a food processor.
Make Ahead Tip: Cover the puree with parchment paper or foil and keep warm over a pan of barely simmering water for up to 1 hour. (Alternatively, cover and refrigerate for up to 2 days; reheat in the microwave.)