First, make the enriched dough: Mix the flour, granulated sugar, yeast, salt, water, and oil in a 6-quart lidded container or a 5-quart stand mixer. Allow the dough to double in size, about 2 hours.
Next, shape the star bread: Divide 2 pounds of the enriched dough into four 1/2-pound pieces. Store the rest of the dough in the refrigerator for another use. Roll the pieces into balls, and let rest for 15 minutes, covered with plastic wrap.
In a small bowl, mix together the brown sugar and cinnamon until well combined. In another bowl, prepare the egg wash by beating the egg with a tablespoon of water.
With a rolling pin, roll out the dough balls into 12-inch circles. Place one of the circles on a piece of parchment paper. Brush with some of the egg wash using a pastry brush, and sprinkle with 1/3 of the cinnamon-sugar mixture.
Place another circle on top of the first circle, and brush with egg wash and sprinkle with another 1/3 of cinnamon-sugar filling. Repeat with one more circle, then place the final circle on top.
Place a small bowl or biscuit cutter, about 2 1/2 inches in diameter, in the center of the circle, and then use a bench scraper to cut the circle into 16 equal strips, cutting through all the layers.
Once you’ve cut all of the strips, remove the biscuit cutter and add a final layer of egg wash to the top to create a nice golden-brown crust.
Take two pieces of dough and twist them away from each other twice. Pinch the ends of the pairs of strips firmly together. Repeat around the whole circle to create the star (you should end up with 8 points).
Transfer the star on the parchment to a baking sheet. Cover the star gently with plastic wrap and let rise for about 1 hour, until a bit puffy. During this time, preheat the oven to 375°F.
Bake for about 30 minutes, until golden brown.
Remove from the oven and brush with soft butter using a pastry brush. Let cool for 15 to 20 minutes.