Spray a lidded plastic container or large glass bowl with cooking spray. Set aside.
In the bowl of a stand mixer fitted with the dough hook, combine flour, sugar, yeast, pumpkin spice, and salt.
Heat milk and butter in a small sauce pan until butter is melted.
Let cool to 115℉/46℃.
While milk mixture is cooling, whisk egg and pumpkin together in a small bowl. Set aside.
With mixer on low speed, pour cooled milk mixture in with dry ingredients.
Add pumpkin mixture.
Continue on low speed for 1-2 minutes, or until ingredients are mixed together.
Increase speed to medium high and knead for 6-8 minutes, or until dough is smooth and pulls away from the sides and bottom of the bowl.
Place in prepared container and cover. Alternatively, you can place the uncovered container or bowl in a dough proofer with a humidity tray set to 78℉/26℃.
Set aside to rise in a warm place (78℉/26℃) until doubled in bulk, about 1½-2 hours.