Preheat oven to 400 F
Peel Parsnips. Using a mandolin, slice parsnips to 1/8 thin slices. This thinner the slices the better. If you don't have a mandolin, slice them as thinly as possible.
Thinly slice the onion.
Grate the cheese.
Generously grease a 6x 9 inch baking dish with butter.
Layer the parsnips and onion and 1/2 of the cheese and 1/2 of the thyme, reserving the bigger pieces of parsnips for the final 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.
In a small pot heat 3 Cups whipping cream. Whisk in salt, nutmeg, the remaining thyme, white pepper, flour and the garlic and when it just comes to a simmer, pour over the layered parsnips, slanting the baking dish to get the cream in all the nooks and crannies. Sprinkle the remaining cheese over the top, a few more leaves of thyme and a little sprinkling of nutmeg. Cover securely with a lid or foil and bake for 50 minutes on the middle rack. Remove foil, pierce with fork, parsnips should be al dente. (If not- your parsnips were perhaps cut thicker that 1/8 of an inch, and you may need to cook longer with the foil on. ) Don't worry if it seems watery at this point, 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 and thickens.