In the bowl of an electric mixer fixed with a whisk attachment, add the warm water and a pinch of sugar. Sprinkle the yeast over the water and let sit for 5 to 10 minutes, until the the mixture begins to foam and bubble. Add the milk, pumpkin, sugar, butter, salt, egg, and pumpkin spice and mix together on low. Once combined, switch to a dough hook. Add the flour a cup at a time, until a smooth and slightly sticky dough forms. Transfer dough to a lightly greased large bowl, cover with plastic wrap, and set in a warm place to rise, about 1 1/2 hours. Meanwhile, make the sugar paste topping.
In a medium-sized bowl, cream together the sugars and the shortening. Add the flour and vanilla and continue to mix until a smooth paste forms. Cut the paste into two equal portions. Form one into a small disc, wrap in plastic, and store in the refrigerator. Leave the second half in the bowl, sprinkle with cocoa powder, and blend together until fully incorporated. Wrap the second piece in plastic and store in the refrigerator until ready to use.
Set the oven to 350 degrees. Line two baking sheets with parchment paper.
Once the dough has risen, punch it down, and transfer to a lightly floured work surface. Sprinkle the top of the dough with flour and shape with your hands or a rolling pin into a rough 12- by 18-inch rectangle. Using a sharp knife, cut into 16 equal portions. Form each piece into a rounded bun by folding the edges under until a smooth round shape takes form. Transfer to a lined baking sheet and continue with remaining pieces of dough.
Take the sugar paste out of the refrigerator and transfer to a lightly floured work surface. Pinch off a quarter sized portion and roll out into a thin round, about 1/8-inch thick. Using a sharp knife or a biscuit cutter, cut a clean circle – about 3 inches wide – and discard the trimmings. Using the knife or biscuit cutter, cut little curves or lines in the paste. Or make little jack-o-lantern faces. Use a spatula to gently transfer the sugar paste design to the top of a piece of dough. If the paste has trouble sticking, lightly dot the top of the dough with water. Repeat with remaining paste until all the buns are topped. Set the buns in a warm place and let rise again for another 30 to 40 minutes.
Bake the buns for 18 to 20 minutes or until the sugar tops are set and the bottom of the buns just barely begin to brown. Remove from the oven and transfer to a cooling rack. Serve warm with spiced coffee or tea.