Stir yeast into water in a large bowl. Allow to rest for 5-10 minutes before stirring to combine (it should get thicker and begin to bubble). Stir in the milk, egg, pumpkin, butter, 1 1/4 c. flour, brown sugar, granulated sugar, salt, cinnamon and pumpkin pie spice. Beat vigorously with paddle attachment for 2 minutes.
Attach dough hook to mixer. Slowly add the rest of the flour, a little at a time, until the dough is stiff enough to knead.
Turn dough onto a floured surface. Knead, adding flour if necessary, until the dough is smooth and elastic. Place dough into a greased bowl (olive oil is fine), turn the dough to coat the entire ball.
Cover with plastic wrap and allow to rise until doubled, approximately 1 hour. If the dough is has not doubled by then, allow it to rise for an additional half hour.
Meanwhile, prepare the filling by combining the sugar, cinnamon and pumpkin pie spice in a small bowl. Set aside.
Transfer the risen dough to a floured surface and roll into a 16″x 12″ rectangle. Combine and spread butter, pumpkin & vanilla extract over dough. Sprinkle with sugar mixture. Roll into log and cut into 15 slices using a sharp knife or dental floss. Place slices into a 9×13 or two 8 or 9 inch round cake or pie pans with the bottoms lined with parchment paper. Cover with a towel and let rise until almost doubled, about 45 minutes.
Preheat oven to 375 degrees. Bake the for 20-25 minutes or until rolls are golden brown (don’t worry if the filling rises and bubbles, it will go down once the rolls have been removed from the oven).
While rolls are baking, prepare frosting by beating the cream cheese and vanilla until smooth.
Slowly add the powdered sugar, then the milk. Beat until combined.
Remove rolls from oven and let cool on wire rack. Frost 5-10 minutes after removal.
Notes
-These rolls would be excellent with standard frosting or even maple frosting on top!