Combine dry ingredients in workbowl of food processor. Process for five seconds.
Add butter and 3 whole eggs. Process for 10 seconds.
With the machine running, pour, don't drizzle, 1/2 cup milk and 1/3 cup water into the mixture. Process for 30 seconds.
The dough will be very wet and sticky, almost like a batter.
Grease a large bowl with butter and scrape the dough into it. Cover with plastic and let the dough rise 2-3 hours, until doubled.
Deflate the dough, shape into loaves (using only a little flour to coat your hands) and place in 2 buttered 8x4" loaf pans for two smallish loaves.
Alternatively, use one 5x9" loaf pan for a single big loaf.
Let rise one hour.
Preheat oven to 400 degrees F. Mix reserved 2 tbs milk and egg yolk and brush the tops of the loaves with this mixture. Bake the brioche for about 30 minutes, until slightly browned.