For the Dough

• In the bowl of a stand mixer fitted with the dough hook, mix the bread flour, sugar, yeast, and salt on low speed for about 30 seconds.
  4½ cups bread flour, ⅓ cup granulated sugar, 1 tablespoon instant dry yeast, 1 tablespoon kosher salt
• Add eggs and milk and mix until a ball forms around the dough hook, about 4 minutes. Increase the speed to medium and mix until the dough is very smooth, about 5 more minutes.
  4 large eggs, 1 large egg yolk, 14 tablespoons whole milk
• Add the butter, 1 tablespoon at a time, while mixing the dough on medium speed. Incorporate the butter after each addition. It should take about 3 minutes to add all the butter.
  18 tablespoons unsalted butter
• Place the dough in a large, oiled bowl and cover with plastic wrap. Set the bowl in a proofing oven or somewhere warm for the dough to rise, about 1-1½ hours. The dough is very enriched so it may not rise very much.
• While the dough rises, prepare the filling: Combine the melted butter, brown sugar, granulated sugar, cinnamon, pie spice and salt. The mixture will firm to a spreadable consistency when kept at room temperature until ready to use. Stir right before using.
  12 tablespoons unsalted butter, 9 tablespoons brown sugar, ¼ cup granulated sugar, 3 tablespoons ground cinnamon, 1 teaspoon pumpkin pie spice, ¼ teaspoon kosher salt
• Line a baking sheet with parchment. Transfer the dough to the baking sheet and pat it out into a 1-inch-thick rectangle. Cover the dough with plastic wrap.
• If making the rolls the day of serving, refrigerate the dough for 1 hour or freeze up to 20 minutes. If making the rolls the next day, refrigerate the rolls overnight.
• When ready to bake, preheat oven to 375°F and grease a 9x13-inch baking pan with softened butter.
• Lightly flour a work surface, and transfer the dough to onto it. Make sure the parchment has been removed from the dough. Lightly flour the top surface of the dough, and roll the dough out into a ½-inch thick rectangle.
• Use an offset spatula to spread the filling mixture, to the edge, evenly over the dough. The top surface of the dough should be covered.
• Roll the dough, beginning with the long side closest to you, into a tight spiral, keeping the roll tight as you work.
• Use a serrated knife or waxed floss to cut the dough log into 1½-inch rolls. Arrange the rolls on the prepared baking dish, leaving ¼-inch between them.
• Loosely cover the rolls with plastic wrap and place in a warm place or proofing oven to rise, about 30-45 minutes.
• In a small bowl, whisk together 1 egg and 1 tablespoon milk. Brush the top of the rolls with the egg wash and bake at 375°F for 25-30 minutes or until the rolls are golden and the internal temperature registers 190°F.
  1 large egg, 1 tablespoon milk
• While the rolls bake, mix together the frosting ingredients and cover with plastic wrap until ready to use.
  2 cups powdered sugar, 6 tablespoons heavy cream, 1 teaspoon pure vanilla extract, ⅛ teaspoon table salt
• When the rolls are finished baking, allow them to cool 10 minutes, then drizzle the icing on top.
• Serve warm (if possible) or reheat in a 350°F oven (loosely covered with foil) about 15-20 minutes before serving.