Combine 1/2 cup flour and yeast; add 1/4 cup warm water, stirring until dry ingredients are moistened and dough forms a soft ball. Make 2 crossed slashes, 3/4-inch deep, in top of dough ball. Place dough ball in remaining warm water; set aside 5 minutes or until dough ball rises to surface. Remove dough from water, and place in a greased bowl. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in bulk.
Combine remaining flour, sugar, and salt. Make a well in center of flour mixture, and stir in eggs and milk. Beat vigorously for 3 minutes or until mixture forms a smooth, shiny paste.
Cream butter; add butter and dough ball to paste, mixing thoroughly. Place in a well-greased bowl; cover tightly with plastic wrap, and refrigerate overnight.
Punch dough down, and turn out onto a lightly floured surface. Set one-third of dough aside; lightly knead together the remaining dough 4 to 5 times. Shape dough into a ball, and place in a well-greased 5 cup brioche mold.
Shape reserved portion of dough into a ball, rolling one end to form a tapered, teardrop shape. Set aside.
Using three floured fingers, press down into center of dough in brioche mold, touching bottom of mold. Enlarge this cavity to shape of tapered end of reserved dough ball. Place tapered end into cavity, rounding upper portion of teardrop to form a smooth ball. Cover and repeat rising procedure 1 hour or until doubled in bulk.
Bake at 375° for 30 minutes; lightly brush with egg white, and bake an additional 10 minutes or until golden brown. Remove bread from mold immediately; cool on wire rack.