Dough

1. In a measuring cup, combine warm milk and yeast.  Gently stir and let sit for 5-10 minutes until the yeast is foamy and activated.
2. Using a paddle attachment in a stand mixer, mix together the melted butter, sugar, pumpkin puree, and egg on low speed.
3. In a separate large bowl, whisk together 3 1/2 cups flour and salt.  Add half of the dry ingredients to the wet ingredients and stir on low speed.  Add in the activated yeast/milk mixture.  Then add the remaining dry ingredients.  Switch to the dough hook attachment and beat at a medium-low to medium speed until the dough is smooth, elastic and begins to pull away from the sides of the bowl.  If needed, gradually add in the remaining 1/2 cup of flour if the dough appears sticky. 
4. Grease a large bowl with cooking spray and place dough in the bowl, turning over once to grease all sides.  Cover with plastic wrap and let rise in a warm location for about 1 hour or until doubled in size.
5. Lightly punch down the dough and let rest for 5 minutes.  Turn out onto a lightly floured work surface and roll into an 14×18″ rectangle, with the shorter length closest to you.

Filling & Assembly

1. In a small bowl combine brown sugar and pumpkin pie spice.
2. Spread the softened butter evenly over the rolled out dough, leaving a 1/2 inch boarder on the farthest edge.  Sprinkle the sugar mixture on top of butter.  Brush the beaten egg on the boarder without filling.  Starting with the edge closest to you, roll the dough into a log and pinch the end seam together to seal the rolls.  Use a large serrated knife to trim each edge of the log to make the ends clean.  Then slice into 12 rolls and place cut side up into a lightly greased 13×9″ pan.
3. Let rolls rise in a warm area until they are puffed and toughing each other, about 30-60 minutes.
4. Preheat oven to 350°F.  Bake for 25 minutes, until rolls are lightly golden brown.  Allow to cool for 10 minutes before applying frosting.

Frosting

1. Beat together the softened cream cheese and butter until creamy.  Add in powdered sugar and mix on low speed.  Add in the vanilla bean paste and beat until frosting is light and smooth.  If needed, gradually add in milk to thin frosting.  Spread onto warm rolls.