Directions:

1. Combine milk & eggs in large bowl of stand mixer; sprinkle with yeast. Let stand 10 minutes or until foamy and frothy. Meanwhile, beat 3 of the eggs in medium bowl until blended. At low speed with paddle attachment, if available, beat eggs into yeast mixture in a steady stream about 1 minute.
2. Slowly beat in 2-1/2 cups of the flour and salt until blended. Increase speed to medium; beat 10 minutes to knead, until dough is very smooth, scraping bowl occasionally. (If dough is sticky, resist urge to add more flour.) Dough will eventually begin to pull away from sides of bowl. Let stand 5 minutes.
3. At low speed, slowly beat in butter 2 T at a time. Increase speed to medium, beat 2 minutes or until smooth and shiny and butter is incorporated. If dough is still extremely moist, add up to 1/4 cup additional flour as necessary. Place dough in small buttered bowl; cover and refrigerate at least 4 hours or overnight. (Dough should double in size.)
4. Gently punch down dough. On lightly floured surface, press dough into 8-inch square. Roll up into log; place, seam-side down, in buttered 8x4" loaf pan. Cover with buttered plastic wrap; let rise in warm place 1 hour to 1 hour 30 minutes or until dough rises to top of pan.
5. Meanwhile, heat oven to 375°F. When brioche has risen, bake 20 minutes.
6. Meanwhile, beat remaining 1 egg until frothy. Lightly brush brioche with egg; bake an additional 10-15 minutes or until deep golden brown and loaf sounds hollow when tapped on bottom. Cool on wire rack.