In a glass measuring cup, measure 1/2 cup of milk. Warm in the microwave until the temperature reaches 115 degrees. (mine took 20 seconds but all microwaves differ) Stir in the yeast and 1 teaspoon of sugar. Set aside and allow to proof 5-10 minutes.
In the bowl of a stand mixer with paddle attachment, mix together remaining 1/3 cup of sugar, egg, pumpkin puree and spices. Turn the mixer to low, pour in milk mixture, add the vanilla.
Switch to the dough hook, add salt and flour, mixing until the dough forms and pulls away from the sides of the bowl. Knead in the mixer 3 - 5 minutes. The dough will be slightly sticky.
Grease a large bowl, transfer the dough to the bowl, cover and rise for 1 hour or until doubled in size.
Punch down the dough, on a lightly floured surface roll the dough to roughly 9"x18". Rub the entire surface with the softened butter. Sprinkle generously with the cinnamon sugar.
Starting at one of the shorter edges, roll into a tight log and pinch the seams to seal.
Place the dough seam side down in a lightly greased 9"x5" loaf pan. Cover and allow to rise for an additional 90 minutes or until rising a couple of inches above the sides of the pan.
Preheat the oven to 350F. In a small bowl whisk the egg and 2 teaspoons of water together, brush over the exposed dough.
Bake 35-40 minutes.
Cool in the pan for 10 minutes, transfer to a cooling rack to cool completely.