In a large mixing bowl or the bowl of a stand mixer, dissolve 2 1/2 teaspoons instant dry yeast in 2 tablespoons warm water.
Add the 1 cup pumpkin puree, 1/3 cup warm milk, 1/4 cup softened butter, 1 large egg2 tablespoons brown sugar, and 1/4 teaspoon salt to the yeast mixture. Stir or mix on low until well combined.
Gradually add flour, 1/2 cup at a time, mixing after each addition, until a soft dough forms. You may need between 3 1/2 to 4 cups of flour depending on the humidity and moisture in the pumpkin puree.
Knead the dough by hand on a lightly floured surface or with a stand mixer using a dough hook for about 5-7 minutes, until the dough is smooth and elastic.
Place the dough in a lightly greased bowl, cover it with plastic wrap or a clean kitchen towel, and let it rise in a warm place for 1 hour, or until it has doubled in size.
Punch down the risen dough and divide it into three equal portions. Roll each portion into a long rope, about 18 inches long. Lay the three ropes side by side on a lightly greased baking sheet. Pinch the ropes together at one end and braid them. Once braided, pinch the other end to seal.
Cover the braided dough with a clean towel and let it rise again for 30 minutes, or until it has puffed up.
Preheat the oven to 350°F (175°C). Brush the braided dough with the lightly beaten egg. Bake for 25-30 minutes, or until the bread is golden brown and sounds hollow when tapped on the bottom.
Transfer the bread to a wire rack to cool completely before slicing and serving.