In the bowl of a stand mixer, add the dry ingredients. Whisk until well combined. Add the eggs to the bowl. Hold back on the butter for now. Using the dough hook attachment, mix to make a smooth, stretchy dough that cleans the sides of the bowl; this should take 7 to 10 minutes at medium speed. 

Once the dough has developed some strength and elasticity, add one piece of the butter and mix at medium speed until it’s fully incorporated into the dough, 1 to 2 minutes. Scrape the bowl if necessary, then continue adding the butter one piece at a time, mixing to incorporate fully before adding the next piece. This dough takes longer than most to develop so be prepared to let the dough knead for another 5 to 10 minutes, or until it has formed a soft, smooth ball.

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.

Generously grease two standard loaf pans,

Remove dough from from the fridge. Divide the chilled dough into 2 equal pieces. Then divide each into 3 equal pieces for each loaf.

To form each loaf, place 3 of the pieces on a lightly floured work surface and roll each piece into a 14" log. Form the logs into a simple three-strand braid, tucking the ends under at each end to seal.

Place the formed dough braids into the greased pans, cover lightly, and let rise for 2 1/2 to 3 hours, until it's doubled and looks very puffy.

Once the loaves have risen to nearly reach the rim of the pan, preheat the oven to 350°F.

In a small bowl, whisk together the egg white along with the milk. Using a pastry brush, lightly coat the top of each loaf with the mixture.

For easy handling, set the loaf pans on a baking sheet. Bake for a total of 30 to 35 minutes. To avoid over browning, tent with foil after the initial 15 to 20 minutes.

Bake until the internal temperature reaches at least 190°F in the center. If you prefer a crustier loaf, bake until the internal temp reaches 205°F.

Remove the pans from the oven. After 10 minutes, remove the bread from the pans and place them on a wire rack.

Enjoy while still warm from the oven. If planning to store the bread, allow it to cool completely before wrapping.

Store any leftovers in an air-tight container at room temperature for up to 3 or 4 days. Or in the refrigerator for 6 to 7 days.

To freeze a whole loaf or slices, wrap the brioche in plastic wrap and heavy-duty foil and store in a freezer bag for up to 3 months