Cook the Leeks: Split the 2 leeks in half lengthwise. Wash well between all the layers, and slice thinly. Melt 1 tablespoon of butter in a medium-sized skillet over medium heat. Add the sliced leeks, season with salt and pepper, and cook, stirring often, until tender but not brown, about 5 minutes. Remove from the heat and reserve.
Steep the Cream: In a 1-quart heavy-bottomed sauce pot, heat 4 cups heavy cream, 2 garlic cloves, 4 sprigs fresh thyme, ¼ teaspoon ground nutmeg, 1 bay leaf, a handful of washed green leek tops, 1 teaspoon sea salt and ¼ teaspoon black peppercorns to a simmer. Let the cream simmer while you build your gratin.
Preheat the oven to 350˚.
Build the Gratin: As you start to assemble the gratin, slice each vegetable layer right before you add it to the dish. This keeps the potatoes and other roots from oxidizing and turning brown while they sit.
Shingle a layer of russet potato slices on the bottom of a 10x13 oven-safe casserole dish, then sprinkle generously with parmesan and a small amount of the leeks, and season with salt and pepper. Repeat this process with the other root vegetables, making sure that every other layer is sliced potatoes. Alternate with a layer of celery root, then potatoes, then sweet potatoes, then potatoes, then parsnips, then potatoes. Any extra root vegetable slices can be used to create a pretty pattern on top.
Strain the cream and gently pour it over the gratin, being careful not to disrupt the layers. Sprinkle the gruyere on top.
Bake the Gratin: Set the gratin dish on a large rimmed baking sheet and cover tightly with a layer of parchment paper, then foil.
Bake for 2 hours total, removing the foil and parchment after an hour and a half, and continue baking until the top is golden brown and the sauce is bubbling, about 30 minutes.
Serve: Allow it to rest at least 45 minutes before serving. I prefer to make this gratin a day ahead and then reheat before serving, as it looks prettier and holds together better that way. There’s no need to rest it for 45 minutes when reheating.