How to Make It
Bring a large pot of salted water to a boil over high heat. Add the celery root and boil until tender, about 6 minutes. With a slotted spoon, transfer to a large baking sheet. Add the turnips to the pot and cook until tender, about 5 minutes. Transfer to the baking sheet. Repeat with the pears, cooking them for 2 minutes and transferring them to the baking sheet. Add the beets to the pot and simmer for 15 minutes. Drain the beets and transfer to a large plate. Let cool slightly, then peel and quarter the beets.
Return the pot to the stove. Add the olive oil, and when it's hot, add the garlic, shallot and thyme and cook over moderate heat until softened, about 5 minutes. Add the stock and boil over high heat until reduced to 1 cup, about 5 minutes. Add the celery root, turnips and pears, cover and cook over moderately high heat, folding gently a few times with a heatproof rubber spatula, until heated through. Add the beets and chestnuts and season with salt and pepper. Cover and cook until heated through, about 3 minutes. Gently stir in the butter, transfer the ragout to a bowl and serve.