Late fall and early winter are the best seasons for celery root. The puree should be made on the day it is served; otherwise the vegetables will lose their fresh flavor.Plus: Ultimate Thanksgiving Guide
In a medium saucepan, combine the sugar with 1/2 cup of water and bring to a boil over high heat. Boil for 5 minutes, then add the cranberries and lower the heat to moderate. Simmer without stirring until the cranberries pop and the syrup reduces slightly, about 5 minutes. Set aside.
In a large pot or dutch oven, combine the celery root, potatoes, coarse salt and garlic. Cover generously with cold water, bring to a boil over high heat and cook until tender, about 20 minutes. Drain well. Transfer the vegetables to a food mill or a ricer and puree, adding the milk, butter, table salt and pepper as you go along. Alternatively, mash with a potato masher.
To serve, reheat the cranberries in their syrup. Mound the puree on a platter or individual plates and make a well in the center. Spoon some of the cranberries and their syrup into the well. Serve the remaining cranberries and syrup alongside.
The cranberries can be cooked and refrigerated up to 2 days ahead.