Cut open the pumpkin from top to bottom. Scrape out all the seeds and fibers. Cut the pumpkin into eighths. Carve the meat out in pieces as large as you can, starting about a quarter inch inside the shell. Slice the meat about one-eighth inch thick.
Crush the three garlic cloves, and use them to wipe the inside of a 12-by-8-inch glass baking dish. Discard what's left of the garlic.
Shingle the pumpkin and carrot slices along the bottom of the dish. Sprinkle some of the chopped garlic, white pepper, and parmesan and gruyere cheeses. Lay down more layers of the pumpkin and carrots, with garlic and cheese in between. Finish with a generous layer of the cheeses.
Beat the egg yolks and mix with the half-and-half and nutmeg. Pour the half-and-half over the casserole. Wrap a relatively tight seal of aluminum foil over the top of the dish, and put it in the preheated 350-degree oven for an hour and ten minutes.
Raise the oven temperature to 400. Remove the foil, sprinkle bread crumbs in a thin layer over the top, and return uncovered to the oven. Continue baking until the crust browns.
Remove from the oven and allow to rest and cool for at least fifteen minutes before serving.