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Step 1
In a stand mixer fitted with the paddle attachment, mix the flour, sugar, yeast, and salt on low speed until well combined. Add 4 of the eggs and the milk and continue mixing on low speed to combine. As soon as the dough starts to clump together, remove the paddle attachment and attach the dough hook. (There will still be unmixed egg and flour in the bowl.) Mix on medium speed for 2 minutes. Using a plastic dough scraper or strong plastic spatula, scrape the bowl and hook. Continue to mix until the dough is firm and elastic, about 2 minutes more. The dough may stick to the hook at this point, but that’s OK. Scrape the dough off the hook again.With the mixer on medium-low speed, add half of the butter, a few pieces at a time. Scrape down the bowl and dough hook, and remove the dough hook. Give the dough a few kneads by hand in the bowl, repeatedly folding the dough over on itself, to help incorporate the butter. Reattach the dough hook and add the remaining butter, a few pieces at a time, mixing on medium-low speed. Once all of the butter has been added, increase the mixer speed to medium and mix for 4 minutes. Scrape the dough hook and the sides and bottom of the bowl. Mix again until the dough is smooth, soft, and shiny, about 4 minutes more. You’ll hear the dough slap against the sides of the bowl when it’s ready. (If your kitchen is warm, the dough may seem too loose at this point. Resist the urge to add extra flour, or the brioche may be tough.)
Step 2
Use a plastic dough scraper or a spatula to turn the dough out onto a clean, very lightly floured work surface. The dough will be very moist. Knead it by hand a few times and then form it into a ball by folding the sides into the middle at 12, 3, 6, and 9 o’clock. Flip the dough over, place your palms on either side of the dough, and tuck it under itself, turning the dough as you tuck to form a loose ball with a smooth top. Transfer the dough, smooth side up, to a clean large bowl. Cover loosely with plastic and let the dough rise in a warm, draft-free spot until doubled in size, about 1 hour.
Step 3
Use the dough scraper or spatula to turn the dough out, smooth top down, onto a very lightly floured work surface. Again, form it into a ball by folding the sides into the middle at 12, 3, 6, and 9 o’clock. Flip the dough over, place your palms on either side of the dough, and tuck it under itself, turning the dough as you tuck to form a loose ball with a smooth top. Transfer the dough, smooth side up, back to the bowl. Cover tightly with plastic. At this point, for best flavor refrigerate the dough overnight. Or let it sit out until doubled in size, about 1 hour. The warmer the room, the faster the brioche will rise, so keep an eye on it.
Step 4
If the dough was refrigerated, let it warm to room temperature, about 2 hours.Butter sixteen 3-inch brioche à tête molds (use molds that are 3 to 3-1/4 inches wide across the top and at least 1-1/4 inches high).Turn the dough out, smooth top down, onto a clean work surface. Form the dough into a ball by folding the sides into the middle at 12, 3, 6, and 9 o’clock. Using a scale and a bench knife, divide the dough into 2 equal pieces, about 1 lb. 3 oz. each. Divide each half into 8 equal pieces of about 2-1/2 oz. each, for a total of 16 pieces of dough. Cover the dough with plastic to prevent it from drying out.Roll each piece of dough into a tight ball by cupping your hand over the dough and moving it in a circular motion with the fingers of that hand slightly tucked in.To form the “tête,” or head, hold your hand perpendicular to the work surface, with your fingers straight and tightly together (like you’re going to do a karate chop). Working with one ball of dough at a time (keeping the others covered with plastic), press down onto the ball with the side of your hand about one-third of the way from one of the edges of the dough ball (leaving one-third of the dough to one side of your hand, and two-thirds of the dough to the other side of your hand). Saw back and forth with your hand almost all of the way through until you get a shape that looks like a bowling pin, or a head and body connected by a very thin, almost translucent neck. Holding the dough by the “head,” turn the dough upright so the body is resting on the work surface. Lower the head down into the body, pressing deeply into the body and spreading it with your thumbs and index fingers to make a nest for the head. Tighten the body around the nestled head by tucking and lifting the body up around the head. Gently place the dough in one of the prepared molds, body down. Repeat with the remaining dough. Transfer the molds to a large rimmed baking sheet.
Step 5
Cover the brioches very loosely with plastic. Let the dough rise until almost doubled in size and filling the molds, about 1 hour. It should spring back when gently poked with a finger.Meanwhile, position an oven rack in the center of the oven and heat the oven to 375°F. It is important that the oven be thoroughly heated so the brioches bake evenly.
Step 6
In a small bowl, make the egg wash by beating the remaining 2 eggs plus 1 egg yolk and a pinch of salt. Lightly brush the top of the brioches (without letting the egg wash drip down into the molds or pans, which would make the brioches stick to their molds). Bake until dark golden-brown on top and golden on the sides (you can lift the brioche slightly to peek in at the edge of the mold), about 18 minutes. (The internal temperature should be 190°F.) Let the brioches cool on a wire rack for 10 minutes before unmolding. Serve while they’re still warm to the touch.