Microwave milk to about 110*F, or for about 25 seconds. Add 1/4 cup of the sugar and swirl to dissolve. Add the yeast and transfer to the bowl of a stand mixer fitted with a dough hook. Let mixture sit a few minutes until you notice a few foamy bubbles start to form on top.
Add 8 eggs to the milk mixture, and half the flour. Turn the mixer on low and slowly add the rest of the flour and sugar. Knead a minute or two, until incorporated. Turn the speed up to medium and knead til dough starts to look smooth, 4 to 6 minutes. Add salt and continue to knead until dough is firm, springy and elastic, another 4 to 6 minutes.
At this point you may find your mixer is getting stuck or overheating. Save your mixer by cutting the dough in half before proceeding.
Add butter a few chunks at a time, let it fully incorporate before adding more. If you cut your dough in half, alternate adding butter and adding pieces of the other half of the dough back.
Once all butter is incorporated, continue kneading on medium speed for another 5 to 7 minutes, until the dough is smooth, shiny and elastic. It should look well emulsified and feel a bit sticky.
Lightly grease a large bowl with butter and transfer dough to the bowl. Wrap tightly with plastic wrap and refrigerate until the dough has doubled in size and firmed up, at least 12 and up to 24 hours. (The slow rise will develop better flavor, and the chilling will make the dough easier to handle and shape.)
When you're ready to bake, turn the dough onto a lightly floured work surface. Divide the dough in two.
Flatten each into a rectangle with the long side as long as your bread pan, and about 1 inch thick. Tightly roll the dough from a long edge. Pinch the end of the roll so it's a well sealed, tightly compact log. Tuck the ends under, pinching to seal them as well.
Transfer the loaves to 2 greased (even better, nonstick and greased) loaf pans, seam-side down.
Tightly wrap both pans with plastic wrap and place them in a warm place. Let the dough rise until it touches the plastic wrap, about 2 hours.
Place an oven rack in the middle of the oven and heat to 325 degrees. Beat an egg with 1 teaspoon water and 1/2 tsp salt and brush it over the tops of the dough.
Place loaf pans in the oven and bake, rotating halfway through, until the tops and sides are deep golden brown and bread is baked through completely, about 50 to 65 minutes. (If you have a probe thermometer, it should register 200 degrees when inserted into the center of the loaf.) If the loaves seem to be browning too quickly, tent lightly with foil.
Remove brioche from their pans and place on a wire rack to cool completely. (If left to cool in the loaf pans, the bottoms and sides will steam and become soggy.) Brioche, if wrapped tightly in plastic, will keep at room temperature for 5 days, refrigerated for 1 week and frozen for up to 1 month.
