Cheese Brioche Buns

To make the dough: Cut the cheese into chunks. Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Place the flour and cheese into the work bowl of a food processor. Process until the cheese is finely ground, and no chunks remain., Combine the flour/cheese with the remainder of the dough ingredients, mixing to make a rough, sticky dough. Knead the dough — in a mixer or bread machine — until it's smooth and starting to become shiny. It can take up to 20 minutes of kneading in a stand mixer to develop (see "tips," below), so we don't recommend kneading this by hand., Form the dough into a ball, place it in a greased bowl, cover, and let it rise for 1 hour., Refrigerate the covered dough overnight, to make it easier to shape., Next day, remove the dough from the refrigerator about an hour before you want to shape the buns., The next day, remove the dough from the refrigerator, and divide it into 10 pieces (about 85g each)., Divide the dough into 10 equal pieces; each will be about 85g., Shape each piece into a ball; working with the chilled dough is exactly like working with clay or Play-Doh, so it's easy to shape. Position the balls on a parchment-lined baking sheet, leaving space between them. Using the bottom of a measuring cup or other flat surface, flatten the balls to about 3 1/2" diameter., Cover the buns, and let them rise until they're quite puffy. This may take up to 3 to 4 hours, depending on how warm your rising environment, and how cold the dough., Towards the end of the rising time, preheat the oven to 350°F., To make the egg wash: Whisk together the egg white and water until foamy. Brush the buns with the egg wash., Bake the buns for 20 minutes; tent loosely with aluminum foil. Bake for an additional 7 to 10 minutes, until the buns are golden brown, and a digital thermometer inserted into the center of one reads about 190°F., Remove the buns from the oven, and cool them on a rack.