• In a small bowl, sprinkle the yeast over the warm milk and water. Stir to combine and let sit until frothy, about 10 minutes.
• In the bowl of a stand mixer fitted with a dough hook or a large bowl, combine the flour, brown sugar, pumpkin pie spice, and salt.
• Slowly mix in the frothy yeast with the milk and water, followed by the pumpkin puree, softened butter, and egg to form a soft dough.
• On a lightly floured surface, knead the dough until smooth and elastic. Transfer to an oiled large bowl, turning to coat. Cover and allow to rest at room temperature until doubled, about 1-2 hours.

To Assemble:

• Grease a pullman loaf pan with a 1 pound (450 gram) capacity with butter.
• In a small bowl, combine the brown sugar and cinnamon.
• On a lightly floured surface, roll the rested dough into a rectangle about 9 inches (23 centimeters) across and 12 inches (30 centimeters) long.
• Brush the top of the rectangle with the softened butter, leaving a 1/2 inch (1.25 centimeter) border around the edges.
• Evenly cover with the brown sugar and cinnamon mixture.
• Fold in about 1/2 inch (1.25 centimeters) of each long end to form a border.
• Roll up the bread into a log shape, short end to short end, sealing the seam to close.
• Place the rolled up loaf seam side down in the prepared loaf pan.
• Cover with a towel and allow to rest at room temperature until the dough has nearly risen to the top of the pan, 45 minutes to 1 hour.
• Preheat oven to 375˚F (190˚C). Place the oven rack on the lower third of the oven.
• Place the loaf pan on a rimmed baking sheet and bake in the preheated oven until the top is deeply golden and the bread sounds hollow when tapped, 30-40 minutes.
• Allow the bread to cool to room temperature before slicing and serving.