Step 1

For the dough: in the bowl of a stand mixer with the whisk attachment, whisk the egg yolks, whole egg, sugar, butter, and buttermilk. Add approximately 2 cups of the flour along with the yeast and salt; whisk until moistened and combined. Remove the whisk attachment and replace with a dough hook. Add all but 3/4 cup of the remaining flour and knead on low speed for 5 minutes. Check the consistency of the dough, add more flour if necessary; the dough should feel soft and moist but not sticky. Knead on low speed 5 minutes more or until the dough clears the sides of the bowl. Turn the dough out onto a lightly floured work surface; knead by hand about 30 seconds. Lightly oil a large bowl. Transfer the dough to the bowl, lightly oil the top of the dough, cover and let double in volume, 2 to 2 1/2 hours.

Step 2

Combine the brown sugar, cinnamon and salt in a medium bowl. Mix until well incorporated. Set aside until ready to use.

Step 3

Butter a 9 by 13-inch glass baking dish. Turn the dough out onto a lightly floured work surface. Gently shape the dough into a rectangle with the long side nearest you. Roll into an 18 by 12-inch rectangle. Brush the dough with the 3/4-ounce of melted butter, leaving 1/2-inch border along the top edge. Sprinkle the filling mixture over the dough, leaving a 3/4-inch border along the top edge; gently press the filling into the dough. Beginning with the long edge nearest you, roll the dough into a tight cylinder. Firmly pinch the seam to seal and roll the cylinder seam side down. Very gently squeeze the cylinder to create even thickness. Using a serrated knife, slice the cylinder into 1 1/2-inch rolls; yielding 12 rolls. Arrange rolls cut side down in the baking dish; cover tightly with plastic wrap and store in the refrigerator overnight or up to 16 hours.

Step 4

Remove the rolls from the refrigerator and place in an oven that is turned off. Fill a shallow pan 2/3-full of boiling water and set on the rack below the rolls. Close the oven door and let the rolls rise until they look slightly puffy; approximately 30 minutes. Remove the rolls and the shallow pan of water from the oven.

Step 5

Preheat the oven to 350 degrees F.

Step 6

When the oven is ready, place the rolls on the middle rack and bake until golden brown, or until the internal temperature reaches 190 degrees F on an instant-read thermometer, approximately 30 minutes.

Step 7

While the rolls are cooling slightly, make the icing by whisking the cream cheese in the bowl of a stand mixer until creamy. Add the milk and whisk until combined. Sift in the powdered sugar, and whisk until smooth. Spread over the rolls and serve immediately.