In the bowl of an electric mixer, combine half of the flour, sugar, yeast, pumpkin pie spice, and salt.
Combine butter and milk in a small saucepan.
Heat over low heat until butter melts.
Cool to 115℉/46℃.
With mixer running, pour milk mixture into flour mixture.
Increase speed to medium and beat for 2 minutes.
Change to dough hook, if using.
Add remaining flour, egg, and pumpkin.
Knead on medium speed 6-8 minutes, or until dough is smooth and pulls away from the bowl.
Spray a covered container with cooking spray.
Turn dough into container.
Allow to rise until doubled in bulk, 1-2 hours.
While dough is proofing, make filling.