The day before baking, make the brioche dough: Start by weighing your flour or measuring it by gently spooning it into a cup, then sweeping off any excess. In the bowl of a stand mixer fitted with the dough hook, mix the flour, sugar, and salt on low speed to combine. Add the yeast and mix to combine, 10 to 15 seconds more. Add the eggs and milk and mix for about 4 minutes on low speed. The dough should form a sticky, shaggy ball around the hook. , Increase the speed to medium and slowly add the butter 1 tablespoon at a time, being careful to incorporate each addition before adding the next; the entire process should take 8 to 10 minutes. As you go, scrape the bowl down once or twice to make sure everything is homogenous. Once all the butter is incorporated, continue to mix the dough until it’s smooth and uniform, 1 minute more. The dough will be quite soft., Grease a large bowl with nonstick spray. Scoop the soft dough into the bowl, cover tightly, and refrigerate for at least 12 hours and up to 18 hours. (The dough will not rise much, if at all, during this time.) , The next day, assemble the buns: On a generously floured surface, gently pat then roll out the dough into a rectangle about 1/2"-thick and 20" x 12" in size (no need to be precise). The dough will still be quite soft at this point and may crack as you roll; it won't have the strength of typical brioche dough; that's OK. Brush the surface of the dough with about 3 tablespoons (roughly 42g) of the melted butter and sprinkle about 2 tablespoons (roughly 20g) of the maple sugar evenly over the ­­top. , To do a 4-fold (book fold): Position the dough so that one of the long sides is facing you. Using a bowl scraper or bench knife to help lift the fragile dough, fold the left edge over toward the center, about 3/4 of the way over the dough. Then repeat on the right side, folding the other edge 1/4 of the way over the dough so that it meets the other section. The dough will now look like an open book with an off-center spine. Use your tool to help fold the dough in half, with the larger side covering the smaller side. Wrap the dough tightly and refrigerate it for 10 to 15 minutes, which will help the butter solidify. The dough will become smoother and stronger with each additional fold., To do a 3-fold (letter fold): Roll out the dough again to a rectangle about 1/2"-thick and 20" x 12" in size. (It's OK if the dough cracks or still feels sticky at this point; use additional flour and a bit of patience to continue with the folding process.) Brush the surface of the dough with another 3 tablespoons (42g) of the melted butter and sprinkle another 2 tablespoons (20g) of the maple sugar on top. Position the dough so that one of the long sides is facing you. Use the bowl scraper or bench knife to fold the left edge of the dough 1/3 of the way over the dough. Do the same with the right edge, resting it on top of the piece you just folded over, as if you were folding a business letter. You will now have 3 layers of dough. Wrap the dough tightly and refrigerate it for 10 to 15 minutes. , Repeat steps 4 and 5 to complete another 4-fold, chilling the dough and using additional flour as necessary if it feels soft or sticky. , Repeat step 6 to complete another 3-fold. , Lightly grease 16 muffin cups with nonstick spray. (If you only have one muffin pan, see “tips” below.) , To shape the rolls: On a lightly floured surface, roll out the dough into a 1/2"-thick rectangle about 12" x 20" in size. Cut the dough lengthwise into 16 strips that are 20" long and 1/2" to 3/4" wide. (The dough can also be cut widthwise into 16 strips that are 12" long and about 1 1/4" wide.) Tightly roll each strip up into a spiral and place it, spiral side up, in the prepared muffin pan. The spiral will be squished tightly into the prepared pan. , Cover the pan with greased plastic wrap or your favorite reusable wrap, and let the buns rise until they appear puffy, 30 to 45 minutes. While they proof, preheat the oven to 375°F with racks in the upper and lower thirds. , Sprinkle the brioche buns with the remaining maple sugar. Bake for 25 to 33 minutes, rotating the pans from front to back and top to bottom at the halfway mark, until the buns are evenly golden brown all over and the internal temperature reads 190°F on a digital thermometer. Cool for 15 minutes in the pan before unmolding and serving. , Storage information: Store brioche buns, covered at room temperature, for up to 2 days. Reheat on a parchment- or foil-lined baking sheet at 350°F, uncovered, for 10 to 15 minutes.