Dough

1. Warm milk and butter until about 100 degrees F (38 degrees C), or until lightly warm to the touch. Transfer to a large mixing bowl and add 2 cups flour, sugar, egg, yeast, and salt. Fold together until the batter forms a dough. If the dough is too sticky, add more flour by the tablespoonful until it begins to form a ball. On a lightly floured surface, place the the dough and knead until smooth and elastic, about 5-8 minutes. Form into a ball.
2. Transfer the dough to a lightly oiled bowl. Cover and allow the dough to rise in a warm environment until doubled in volume, about 2 hours.

Filling and Assembly

1. Preheat oven to 375 degrees F (190 degrees C).
2. In a small bowl, mix together the brown sugar, cinnamon, and butter until it forms a uniform spread. Set aside.
3. On a lightly floured surface, roll out the dough to approximately an 11 x 15-inch rectangle. Using an offset spatula, spread the brown sugar mixture uniformly on the dough, leaving a 1/2-inch border around the edge. Starting lengthwise, roll the dough until coiled. Pinch together the edges to seal.
4. Using a sharp serrated knife, cut the coil in half lengthwise and face the inside upwards. Pinch together one end of the dough and braid the two long strands, facing the cut side upwards at all times. Pinch together the remaining end. Form the dough into a circular shape and pinch together the pinched ends. Transfer the circle to a lightly greased cast-iron pan or 10-inch round cake pan and brush with the beaten egg. Bake for 25-30 minutes, or until dark brown and fragrant.
5. Run a knife around the outside of the pan and allow to rest for 15-20 minutes before serving.