Prepare the Dough:
In a small bowl, combine warm milk, yeast, and 1 tbsp of sugar. Let sit for 5-10 minutes until frothy.
In a large mixing bowl, combine the pumpkin puree, melted butter, egg, remaining sugar, salt, and pumpkin pie spice. Mix until smooth.
Add the yeast mixture to the bowl and mix until combined. Gradually add the flour, 1 cup at a time, until a soft dough forms.
Knead the dough on a floured surface for about 5-7 minutes until smooth and elastic. Alternatively, use a stand mixer with a dough hook for 5 minutes.
Place the dough in a greased bowl, cover with a damp towel, and let rise in a warm place for 1 hour or until doubled in size.
Prepare the Filling:
In a small bowl, mix the softened butter, brown sugar, cinnamon, and pumpkin pie spice until well combined.
Assemble the Buns:
Punch down the risen dough and roll it out on a floured surface into a 12x18-inch rectangle.
Spread the cinnamon-sugar filling evenly over the dough, leaving a 1/2-inch border around the edges.
Starting from the long side, roll the dough tightly into a log. Cut into 12 equal pieces.
Place the rolls in a greased 9x13-inch baking dish. Cover and let rise for 30 minutes.
Bake:
Preheat the oven to 350°F (175°C). Bake the rolls for 20-25 minutes, or until golden brown and cooked through.
Prepare the Glaze:
In a bowl, beat the cream cheese and butter until smooth. Gradually add the powdered sugar, vanilla, and milk, mixing until a smooth glaze forms.
Serve:
Spread the cream cheese glaze over the warm buns and serve immediately.