To make the brioche: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. In a stand mixer or bread machine (programmed for dough), mix together all of the ingredients to form a smooth, shiny dough. Don't worry; what starts out as a sticky mess becomes beautifully satiny as it kneads. This dough takes longer than most to develop, so be prepared to let the dough knead for up to 15 to 20 minutes in a stand mixer. Also, we don't recommend trying to knead it by hand. If you're using a bread machine, let it complete its kneading cycle, then continue as directed below., Form the dough into a ball (it'll be very soft), place it in a greased bowl, cover the bowl, and it let rise for 1 hour. Then refrigerate the dough for several hours, or overnight. This will slow the fermentation and chill the butter, making the dough easier to shape., Shape the dough into a 9" log, and place it in a lightly greased 9" pain de mie pan. Cover the pan, and let the chilled dough come to room temperature, then rise to within 1 1/2" or so of the rim of the pan; this may take up to 5 hours or so., Towards the end of the rising time, preheat the oven to 350°F., Close the lid on the pain de mie pan, and bake for 45 minutes. Remove the pan from the oven, and remove the lid; the bread should be golden brown, and register at least 205°F on an instant-read thermometer. Continue to bake for a few more minutes if the bread isn't done, then remove it from the oven, turn it out of the pan, and cool completely on a rack., To make French toast: Let the loaf get a bit stale before using it for French toast. Or cut six 3/4" to 1"-thick slices of fresh brioche and let them sit, uncovered, for several hours., Whisk together the sugar, cinnamon, nutmeg, and flour., In a separate bowl or measuring cup, whisk together the eggs, cream or milk, and vanilla., Whisk the wet ingredients into the dry ingredients., Divide the batter among six saucers, and soak each piece of bread for about 2 minutes on each side, until it's absorbed most of the batter, but isn't soggy all the way through. While the bread is soaking, preheat your griddle., Cook the French toast for 2 to 3 minutes on the first side, or until it's golden brown; adjust the heat so it's not cooking too slowly or too quickly. Turn the toast over, and cook the second side until golden brown, about 2 minutes., To serve, spread hot slices with butter, and drizzle with maple syrup.