Because of the super buttery dough, these meltingly tender brioche buns hover on the line between pastry and bread. The recipe comes from Heritage Baking (Chronicle, $29.95), by Illinois bakery owner Ellen King.
Place milk, 4 eggs, 3 cups flour and yeast in the bowl of a stand mixer fitted with the dough hook attachment. Mix on medium speed until dough is smooth and comes together, about 3 minutes, scraping down the bowl after the first minute of mixing, if needed. Let dough rest in bowl 20 minutes to help relax the gluten.
Add granulated sugar and 1 1/2 teaspoons salt; mix on low speed 3 minutes more, scraping dough off the hook after the first minute.
Add half of the 1 cup butter and continue to mix on low until butter cubes are no longer visible and are completely incorporated into dough. Add remaining cubed butter and mix until incorporated.
Once all the butter is added, increase speed to medium and mix until dough makes a slapping sound and comes away from the bowl, about 16 minutes. Be patient and resist the urge to increase the speed. You will start hearing a distinct slapping sound when dough is almost ready.
Transfer dough to a medium bowl coated with cooking spray. Cover with plastic wrap; let stand at room temperature 1 hour, then punch down dough to help redistribute the yeast. Cover again and refrigerate at least 2 hours or overnight.
After the dough has completed its 2-hour rest in the refrigerator, transfer it to a lightly floured work surface and roll out to a 10x6-inch rectangle. Place in refrigerator to chill while preparing filling.
For filling: In a large bowl, whisk together the 1/2 cup room temperature butter, the brown sugar, 1/4 teaspoon salt, cinnamon, orange zest, 1 egg and the 1 tablespoon flour until creamy. Grease a 9x13-inch baking pan.
Roll dough into a 19x15-inch rectangle with the long end facing you. Spread filling over dough. Roll dough away from you to form a long cylinder and pinch seam to seal. Cut into fifteen slices, each about 11/4 inches wide. Arrange rolls in pan cut sides up, about 1/2 inch apart.
Preheat oven to the lowest setting, about 170°. Place a cake pan on the lowest oven rack. Add 1 cup boiling water to cake pan. Turn off oven. Cover rolls loosely with plastic wrap and place on center oven rack for 2 hours to proof.
Remove pan with rolls from oven and remove plastic wrap. Remove cake pan with water from oven. Preheat oven to 350°. In a small bowl, lightly beat 1 egg; brush over rolls. Sprinkle with turbinado sugar, if desired. Bake until golden brown, 25 to 30 minutes, rotating pan halfway through baking. Cool 10 minutes.
For icing: In a bowl, whisk together powdered sugar and milk until smooth, adjusting consistency with extra sugar or milk as needed. Brush over warm rolls and serve. Store leftovers in an airtight container and eat within 2 days.