Dissolve the yeast into the water in a large mixing bowl or bowl of a stand mixer.
Add in the pumpkin, milk, butter, egg, brown sugar and salt. Mix it until it is well combined.
Add flour 1/2 cup at a time until a nice, soft dough forms.
Knead the dough for 5 minutes or so until is smooth and elastic. Place in a lightly greased bowl, cover, and let rise about 1 hour.
Divide the risen dough into thirds. Roll out each third into a long snake or rope (about 18 inches long). Lay the 3 ropes next to each other on a lightly greased baking sheet. One one end of the rope, pinch the 3 strands together and begin to braid. When you've braided the whole thing, pinch the remaining ends together.
Cover and let rise another 30 minutes or so. Brush the braided dough with the lightly beaten egg.
Bake at 350 degrees for about 25 minutes until golden brown. Cool on a wire rack.