Mix the Dough: In a large bowl, combine the active sourdough starter, flour, milk, sugar, egg, and salt. Mix until a shaggy dough forms.

Add Butter: Gradually add the softened butter to the dough, mixing well until the butter is fully incorporated and the dough becomes smooth and elastic.

Knead the Dough: Turn the dough out onto a lightly floured surface and knead for about 5-7 minutes until the dough is smooth and elastic.

First Rise (Bulk Fermentation): Place the dough in a greased bowl, cover with a damp cloth or plastic wrap, and let it rise at room temperature for 4-6 hours, or until doubled in size.

Shape the Dough: After the first rise, turn the dough out onto a lightly floured surface and shape it into a rectangle. Let it rest for 10 minutes.

Roll and Fill: Roll the dough out into a large rectangle (about 12x16 inches). Spread the softened butter for the filling evenly over the dough. Sprinkle the brown sugar, cinnamon, and salt evenly over the butter.

Roll the Dough: Starting from the long side, tightly roll the dough into a log. Cut the log into 12 equal pieces.

Second Rise: Place the rolls in a greased 9x13-inch baking dish, cover with a damp cloth or plastic wrap, and let them rise at room temperature for 2-4 hours, or until doubled in size. Alternatively, you can place them in the refrigerator to rise overnight.

Preheat the Oven: Preheat your oven to 375°F (190°C).

Bake: Bake the rolls for 25-30 minutes, or until golden brown.

Prepare the Glaze: While the rolls are baking, mix the powdered sugar, milk, and vanilla extract in a small bowl until smooth. Add more milk if needed to reach your desired consistency.

Glaze the Rolls: Remove the rolls from the oven and let them cool for a few minutes. Drizzle the glaze over the warm rolls.