Mix the starter ingredients together until smooth, cover, and let rest at room temperature overnight (or for at least 8 hours).
In the morning, combine the starter with all of the dough ingredients until dough is soft smooth. Surface of dough may still be a bit rough and a bit sticky. Grease a large bowl. Cover, and let dough rise for 90 minutes. Deflate the dough and re-shape into a ball and return to the bowl. Cover and let rise for another 90 minutes.
Tip the dough out onto a lightly greased work surface. Divide into 12 pieces then shape into balls. Roll the dough balls under your lightly cupped fingers to tighten up the surface.
Place the rolls on a parchment-lined baking sheet, cover, and let rise for 1 hour or until they are puffy. Next, cover the rolls and refrigerate them for 2 hours.
Towards the end of chill time, preheat the oven to 425°F (218°C). Prepare the egg wash by lightly beating the egg with water until combined and set aside.
Remove the rolls from the refrigerator and brush with the prepared egg wash. Using a very sharp knife or baker's lame, cut a 1/4" (0.6 cm) deep cut across the top of each roll.
Bake the rolls for 25 minutes, or until they are golden brown. Remove from the oven and cool on a rack.