Combine the milk, melted butter, egg, granulated sugar, salt, active sourdough starter, and all-purpose flour until a shaggy dough forms, then knead it on a lightly floured surface for a couple of minutes until smooth and soft, adding a little extra flour only if it is excessively sticky. The dough should come together into a supple ball that feels elastic and looks smoother on the outside.

Cover the dough and leave it in a warm spot to rise overnight until doubled in size, which took about 10 hours in a 76 °F kitchen. It should look fuller, feel lighter, and show some airy softness when gently pressed.

Let the filling butter soften and stir the brown sugar with the cinnamon until evenly blended. The filling should look evenly spiced with no dark cinnamon pockets or dry sugar clumps.

Divide the dough into 4 equal pieces and roll each one into an 8.5-inch circle, then place the first round on a silicone mat or parchment and spread it with 1/3 of the softened butter followed by 1/3 of the cinnamon sugar mixture. Keep the butter thin and even so the layers stay defined without squeezing filling out the sides.

Stack the second and third rounds the same way, finish with the fourth round on top, set a shot glass in the center, and cut from the outer edge toward the glass into 4 equal sections, then into 16 total strips. The center should stay intact under the glass, and the cuts should look clean rather than torn.

Take each pair of neighboring strips and twist them away from each other 2 or 3 times, then pinch the ends together firmly to make a point, repeating until you have 8 points. The shaped star should look even and defined, with sealed tips that hold their shape instead of springing open.

Transfer the shaped star to an 11-12 inch pan, dutch oven, or skillet, cover it with a lid or foil, and let it rise in a warm spot for 1-2 hours. It is ready when it looks puffy, feels aerated, and jiggles slightly rather than feeling dense.

Heat the oven to 350 degrees F, whisk the egg with the water, brush the top of the star, and bake it for 40 minutes uncovered, then cover it with foil and bake 10 minutes more, placing a cookie sheet on the rack below to catch drips. The top should turn deeply golden with a glossy egg-washed sheen and a rich cinnamon aroma as it finishes baking.

Beat the cream cheese, powdered sugar, vanilla extract, and milk until smooth, then drizzle or brush the icing over the warm bread. The icing should loosen enough to flow over the ridges while still clinging to the warm surface.