Add the honey and yeast to the warmed milk. Allow the yeast to bloom for five minutes, or until foamy.
In a large mixing bowl, whisk the yeast mixture into the first quantity of bread flour. The finished sponge should resemble a thick batter.
Cover the mixing bowl with plastic wrap, or a clean kitchen towel, and allow the sponge to rise until it has doubled in bulk in a warm, draft-free area of your kitchen. This should take about 30 minutes.
Develop the Brioche
Transfer the sponge to the bowl of a five quart stand mixer.
With the mixer on low speed, and using the paddle attachment, mix in the eggs, sugar, and salt all at once.
Once the mixture looks like a smooth, thick batter, slowly add the remaining bread flour to the egg-sponge mixture.
After the first two cups, the batter will become too stiff to mix with the paddle attachment, so you need to switch to the mixer's dough hook attachment and mix on the second speed until the dough comes together.
Incorporate the Butter
Begin adding the butter to the dough 2 tablespoons at a time. Add the next 2 tablespoons only when the previous addition has been fully incorporated.
Save the wrappers from your sticks of butter.
Once all of the butter has been incorporated into the dough, the dough should be soft, pliable, and smooth.
Remove the dough from the bowl and, using the saved butter wrappers, grease the inside of the bowl. Discard the wrappers.
Return the dough to the bowl and turn it to cover the surface of the dough with a protective layer of fat.
Cover the bowl and allow the brioche to rise for an hour, or until it's doubled in bulk.
Once the dough has finished rising, punch the dough down to dispel the gases that have developed during the rising.
Pan, Proof, Slash, and Bake
Preheat your oven to 375°F. Lightly grease two loaf pans with baking spray. Combine the beaten egg and water in a small bowl and set aside.
Turn the dough out of the bowl, onto a floured countertop.
Use a bench scraper, or knife, to divide the dough in half.
Form the halves into logs that are the length of your loaf pan and place them into the greased pans.
Use a pastry brush to brush the dough with the egg wash to prevent the surface from drying out.
Place the pans into a draft-free area and allow the dough to rise until the top of the dough is about an inch below the top of the pan. This should take anywhere from 30 minutes to 1 hour.
Brush another thin coat of egg wash onto the tops of the brioche loaves.
If you want a decorative crust, use a lame, or a clean razor blade, to make cuts into the surface of the dough.
Bake the dough for 30-35 minutes, or until the top is a beautiful golden brown and the loaf sounds hollow when tapped.
Remove the pan from the oven and allow it to cool down for 10 minutes.
Turn the baked loaves out onto to a cooling rack and allow them to cool completely before slicing, or wrapping to freeze.
The loaves will stay fresh for up to two days. Wrap them in plastic wrap, or place them into a food storage bag to prevent staling.