Cinna-Buns

Why I Love This Recipe
This recipe is originally from the King Arthur Flour website, although it is no longer available there, and has a few slight changes.
Ingredients You'll Need
1 cup (8 ounces) lukewarm milk
2 large eggs, room temperature
1/3 cup (2 5/8 ounces) unsalted butter, cut up
4 3/4 cups (20 ounces) Mellow Pastry Blend OR 4 1/2 cups (19 1/2 ounces) King Arthur Unbleached All-Purpose Flour
1 3/4 teaspoons salt
1/2 cup (3 1/2 ounces) sugar
2 1/2 teaspoons instant yeast
Filling
1/3 cup (2 5/8 ounces) unsalted butter, softened
1 cup (7 1/4 ounces) brown sugar, packed
3 tablespoons (3/4 ounce) ground cinnamon
Directions
Manual/Mixer Method: Combine all of the dough ingredients in a large mixing bowl, stirring till the mixture becomes cohesive.
Transfer the dough to a lightly oiled work surface, and knead it for 5 to 8 minutes, till it’s smooth. Or knead it in an electric mixer, using the dough hook, for 4 to 7 minutes at medium speed.
Place the dough in a lightly oiled bowl, turn to grease all sides, cover the bowl with a proof cover or plastic wrap, and let it rise for 60 minutes, till it's nearly doubled in bulk.
Assembly: Transfer the dough to a lightly greased work surface, and roll it into a 16 x 21-inch rectangle.
Spread the dough with the 1/3 cup butter. Mix the brown sugar and cinnamon, and sprinkle it evenly over the dough.
Starting with a short end, roll the dough into a log, and cut it into 12 slices. Place the buns in a lightly greased 9 x 13-inch pan. Cover the pan with a proof cover or plastic wrap, and let the buns rise overnight.
Bake the buns in a preheated 400 F oven until they're golden brown, about 15 minutes. While the buns are baking, make the icing.