Serves 4 to 6.   Published September 1, 2007. Cooks Illustrated.
The quickest way to slice the vegetables is in a food processor fitted with an 1/8-inch slicing blade. If the potatoes are too long to fit into the feed tube, halve them crosswise and put them in the feed tube cut-side down so that they sit on a flat surface. If the potato slices discolor as they sit, put them in a bowl and toss with a couple tablespoons of the cream and chicken broth. If you like, use Parmesan instead of cheddar.
 
INGREDIENTS
2 TB butter
1 onion, minced, about 1 cup
1 TB chopped fresh thyme
1 1/2 tsp salt 
1/2 tsp pepper
8 oz celery root (about 1/2), peeled and sliced 1/8 inch thick
8 oz parsnips (about 2 medium), peeled and sliced 1/8 inch thick
1 cup chicken broth
1 cup heavy cream
2 bay leaves
1 1/2 lbs russet potatoes (about 2 large), peeled and sliced 1/8 inch thick
4 oz grated cheddar cheese, 1 cup

INSTRUCTIONS

1. Adjust oven rack to middle position; heat oven to 425 degrees.
2. Melt butter in large Dutch oven over medium-high heat until foaming subsides. Add onion and cook, stirring occasionally, until soft and lightly browned, about 4 minutes. Add garlic, thyme, salt, and pepper; cook until fragrant, about 30 seconds. Add celery root, parsnips, chicken broth, cream, and bay leaves and bring to simmer. Cover, reduce heat to medium-low, and simmer for 5 minutes. Add potatoes, bring mixture back to simmer, cover, and cook until potatoes are almost tender (paring knife can be slipped into and out of potato slice with some resistance), about 10 minutes. Discard bay leaves.
3. Transfer mixture to 8-inch-square baking dish (or other 1 1/2-quart gratin dish) and press into an even layer; sprinkle evenly with cheese. Bake until cream is bubbling around edges and top is golden brown, about 15 minutes. Cool 10 minutes before serving.
4. To Make Ahead: Once the scalloped vegetables have been transferred to the baking dish and pressed into an even layer in step 3, they can be wrapped in plastic wrap and refrigerated for up to 24 hours. When ready to bake, add the cheese, cover with foil, and bake in a 400-degree oven until the mixture is hot and bubbling, about 45 minutes. Remove the foil and cook until the cheddar begins to brown, about 30 minutes longer. Let cool for 10 minutes before serving.