This celery root purée is satiny-smooth, with a natural tang from the apple and just enough curry powder to make it interesting. I like to make a little extra and keep it on hand to thicken vinaigrettes and fold into stir-fries.
Slice off one end of the celery root, making a flat edge so the vegetable doesn't roll around. Cutting in a downward motion, remove the outer skin until the root is completely peeled. Repeat with the other celery root. Cut into even, medium-sized chunks, then place in a stockpot along with milk and enough water to cover the vegetables. Bring to a simmer.
Peel and cut two apples into large chunks. Add to the simmering celery root, along with the caramelized onion, curry powder, turmeric, and a pinch of salt. Simmer until the celery root is completely tender, about 15–20 minutes.
When the celery root and apples are soft and liquid has reduced a bit, taste; add more salt if necessary. Using a slotted spoon, add the solids to the food processor, followed by the liquid (to control the desired smoothness of the puree). Purée, then add butter and another pinch of salt; purée again until smooth. Cut remaining apple into matchstick-sized pieces; garnish purée with apple and walnuts before serving.