Preheat the oven to 400°F (200°C). Butter a 13-by-9-inch baking dish or large gratin dish.
Cook the bacon in a skillet over medium heat until crisp. Transfer to a paper towel-lined plate to drain and cool.
Meanwhile, stir together the cream, chives, salt, pepper, and nutmeg in a large bowl. With a mandolin, a handheld slicer, or a heavy sharp knife, cut the celery root and the potatoes into 1/8-inch-thick slices, adding the slices to the cream mixture as you work to prevent them from discoloring. Using your hands, gently toss the slices to completely douse each one with the cream and to ensure the potatoes and celery root are mingled together.
Arrange half the celery root and potato slices in the buttered dish, pressing down on them gently to make an even layer. Sprinkle with the bacon and shallot. Top with the remaining celery root and potato slices, pouring any cream left in the bowl over the top. Press down on the mixture to make a flat top. Sprinkle the gratin with the cheese and then the bread crumbs.
Bake until the slices are very soft and the gratin is browned and bubbling, about 55 to 60 minutes. Let cool for about 20 minutes before serving to allow the gratin to absorb some more of the cream.