Instructions:
- Gently whisk the active starter, warm milk, sugar, eggs, and melted butter in a large bowl. Gradually mix in the flour and salt until a shaggy mass forms.
- Knead the dough by hand or with a mixer until smooth and elastic (about 8–10 minutes). It should pass the 'windowpane test.'
- Place the dough in a lightly oiled bowl, cover, and let it rest at room temperature for 1–2 hours until slightly puffy (First Rise).
- Punch down the dough, reshape it into a ball, cover tightly, and refrigerate for a minimum of 10 hours, preferably overnight (Cold Fermentation).
- Prepare Filling: Mix the softened butter, brown sugar, cinnamon, and salt together until well combined. Set aside.
- On a lightly floured surface, roll the chilled dough into a large rectangle (approximately 12x18 inches). Spread the cinnamon mixture evenly over the dough, leaving a small border on one long edge.
- Tightly roll the dough up starting from the long edge opposite the border. Pinch the seam closed. Cut the log into 12 equal slices.
- Arrange rolls cut-side up in the greased 9x13 pan. Cover loosely and let them proof in a warm spot for 1.5–2 hours, until visibly puffy and nearly touching (Second Proof).
- Preheat oven to 375°F (190°C). Bake for 20–25 minutes, rotating halfway, until golden brown and cooked through.
- Prepare Glaze: While rolls cool slightly, brown the ¼ cup of butter in a small pan until nutty. Whisk this cooled brown butter into the softened cream cheese, then beat in the powdered sugar and vanilla until smooth. Add milk/cream if too thick.
- Generously slather the warm rolls with the brown butter frosting. Serve immediately.