Mix the dry ingredients. In a mixing bowl, whisk together the flour, brown sugar, yeast, pumpkin pie spice, and kosher salt together.
Warm the milk. In a microwave-safe measuring cup, combine the milk and diced butter. Warm in 20 second increments until the milk is warm, but not hot (110-115 F), and the butter is soft and partially melted.
Mix the dough. In the bowl of a stand mixer or a large mixing bowl, whisk together the egg, vanilla, and pumpkin puree until smooth. Whisk in the milk and butter combination and then pour in the flour mix. Mix on low with a dough hook for 8-10 minutes, until smooth. If mixing by hand, use a wooden spoon to mix until the dough comes together then knead by hand in the bowl for 10 minutes, until the dough is smooth and no longer shaggy.
Proof the dough. Transfer the dough to a greased bowl and cover with plastic wrap. Let the dough rise in warm area until doubled in size, about 90 minutes.
Filling
Mix the filling. In a small mixing bowl, mix together the softened butter, cinnamon, pumpkin pie spice, and brown sugar until smooth and paste-like.
Roll out the dough. On a smooth and clean work surface, roll out the dough into a 16x20 that's about 1/4" thick. Spread the filling in an even layer over the rolled out dough and leave a 1/2" border at the top side of the dough. Roll up the dough into a log, rolling from the longest side, and pinch the seam to close the rolls up.
Cut and proof the rolls. Slide some flavorless floss underneath the log to make your cuts, starting by cutting off and discarding the two uneven ends. Cut the rolls into 12 equal slices about 1 1/2 inches thick. Place the cut rolls in a greased 9x13 baking dish, cover and allow the rolls to rise a room temperature for about an hour.
Towards the end of proofing the rolls, preheat an oven to 350 F.
Bake. Uncover the rolls and drizzle with the heavy cream. Bake for 25-27 minutes, until puffed and lightly golden brown. Remove from the oven and let the rolls cool for 15 minutes.
Mix the glaze. Whisk the glaze ingredients together until smooth and spread over the still-warm pumpkin cinnamon rolls. Serve warm.
Notes
* not to be confused with pumpkin pie filling which has sugar and spices. You only want plain pumpkin puree.