Preheat oven to 400 F.
Peel the Parsnips and using a mandolin, slice parsnips to 1/8 thin slices. The thinner the slices the faster this will bake. If you don’t have a mandolin, slice them as thinly as humanly possible! Thinly slice the onion and grate the cheese. Generously grease a 9 x13 inch baking dish with butter.
Layer the parsnips and onion with 2/3 of the cheese and ⅔ of the thyme -saving the rest for the top- and reserving the more perfect pieces of parsnips for the final top layer. Press down and make sure layers are even. It’s OK if the inside layers are messy. Place the last layer of parsnip slices in nice looking overlapping rows.
Heat 3 cups heavy cream in a small pot, whisking in salt, nutmeg, thyme, white pepper, flour, and garlic. Once it simmers, pour over the layered parsnips, tilting the dish to coat evenly. Top with remaining cheese, thyme, and nutmeg. Cover with foil and bake at 350°F for 50-60 minutes until parsnips are fork-tender. Remove foil and check doneness; if needed, bake longer until parsnips are al dente. Don't worry if it seems watery—it will set.
Once fork tender, remove foil and bake another 15 minutes uncovered , or until golden and bubbly. It is important to let it sit at room temp for 15-20 minutes before serving, so it sets up and thickens.
You can also make this all ahead, and simply reheat before serving.