In a bowl, mix 2 cups flour, sugar, yeast, pumpkin pie spice, and salt.
Warm milk and butter in microwave for 60 seconds. Pour into dry mix.
Add pumpkin and egg. Stir, then add 1½ more cups flour.
Knead dough, adding more flour as needed. Rest 10 mins.
Mix butter and pumpkin for filling. In another bowl, mix brown sugar, cinnamon, and pumpkin spice.
Roll dough into 15×18” rectangle. Spread pumpkin butter, then sprinkle sugar mixture.
Roll into a log and cut into 12 pieces. Place in greased pan.
Let rise 30–45 mins. Bake at 350°F for 22–26 mins.
Beat icing ingredients until smooth. Spread on warm rolls. Serve.