In the bowl of a stand mixer, combine the 2 1/2 teaspoons instant dry yeast, 1 cup cooked and mashed sweet potato, 1/3 cup warm milk, 1/4 cup butter, 1 egg, 3 tablespoons brown sugar and 1/4 teaspoons salt. Mix it until it is well combined.
Add the 3 to 3 1/2 cups all-purpose flour1/2 cup at a time until a nice, soft dough forms.
Knead the dough for 2 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 an egg wash (1 egg + 1 tablespoon water).
Bake at 350 degrees for about 25 minutes until golden brown. Cool on a wire rack.