1. In a large mixing bowl, whisk together your active sourdough starter, warm milk, granulated sugar, melted butter, salt, and egg until well combined. The mixture should look slightly milky and uniform.

2. Gradually add the all-purpose flour, about 1 cup at a time, mixing with a wooden spoon or a stand mixer with a dough hook until a shaggy dough forms. Once all the flour is incorporated, knead the dough for 5-7 minutes until it’s smooth, elastic, and no longer sticky. It should spring back slightly when poked.

3. Place the kneaded dough into a lightly oiled bowl, turning it once to coat. Cover the bowl tightly with plastic wrap or a clean kitchen towel. Let it rise in a warm spot for 8-12 hours, or until doubled in size. For a slower rise and more flavor development, you can place it in the refrigerator overnight (12-24 hours).

4. Once the dough has risen, gently punch it down to release the air. Turn the dough out onto a lightly floured surface. Roll the dough into a large rectangle, approximately 18×12 inches, aiming for an even thickness.

5. In a small bowl, combine the ground cinnamon and brown sugar. Spread the softened butter evenly over the surface of the rolled-out dough, leaving a small border along one long edge. Sprinkle the cinnamon-sugar mixture generously over the butter. Starting from one long edge, tightly roll the dough into a log.

6. Use a sharp knife or unflavored dental floss to slice the log into 12-15 equal pieces, about 1-1.5 inches thick. Arrange the sliced rolls in a greased 9×13 inch baking dish, leaving a little space between each. Cover the dish with plastic wrap or a clean towel and let them rise in a warm place for 1-2 hours, or until they look puffy and have nearly doubled in size.

7. Preheat your oven to 375 F (190 C). Once the rolls have completed their second rise, remove the cover and bake for 20-25 minutes, or until golden brown on top and cooked through. The internal temperature should be around 200-205F.

8. While the rolls are baking or cooling slightly, prepare the frosting. In a medium bowl, whisk together the powdered sugar, milk or cream, and vanilla extract until smooth and creamy. Once the rolls are out of the oven, let them cool for 5-10 minutes, then generously spread the frosting over the warm rolls. Serve immediately.