Dissolve the yeast in the milk and set aside.

In the food processor fitted with the dough blade and dough bowl, pulse together the flour, brown sugar, cinnamon, ginger, salt, allspice, and the nutmeg. Turn the food processor to the on position and feed the eggs and pumpkin puree through the feed tube. Continue to blend the dough until it becomes soft and supple, about 5 minutes. The dough will start to wrap around the blade in a ball.

Leaving the dough in the food processor, let it sit for 30 minutes. After it rests, pulse 4 times. Pull the dough bowl out of the food processor, and then remove the dough blade.

Mound the dough in the center of the dough bowl and place the bowl on a baking sheet lined with parchment or foil. Collect any extra dough from the dough blade, roll into a small ball, and place the ball on top of the larger piece of dough. Allow the dough to rise in a warm place for 2 hours.

Preheat the oven to 350°F. Whisk together the remaining egg and the teaspoon of milk. Brush over the top of the dough. Bake for 30-35 minutes, until the top is a deep golden brown. Remove from the oven and cool slightly before removing from the bowl.