Delicious sourdough cinnamon rolls with a tender brioche‑style dough, brown‑sugar‑cinnamon filling, and a velvety cream‑cheese glaze.
Cut the butter into small pats and let it come to room temperature. In a stand mixer fitted with the dough hook, whisk together the eggs, milk, caster sugar, and sourdough starter. Add the flour and salt, mix on low speed for about three minutes, then let the dough rest for ten minutes. After the rest, increase speed and mix until the dough comes together, adding a little extra flour if needed. Finally, add the butter pats one at a time on low speed until fully incorporated, resulting in a smooth, shiny dough.
Transfer the mixed dough to a covered container and let it ferment at about 75 °F (23 °C) for two hours, performing three to four sets of stretch‑and‑folds at thirty‑minute intervals.
Cover the bulk‑fermented dough and chill it in the refrigerator for at least two hours (or overnight) until it is completely cold and firm.
Prepare the filling by mixing light brown sugar, all‑purpose flour, melted unsalted butter, ground cinnamon, and a pinch of salt. Lightly flour a work surface, roll the chilled dough into an 11 × 21 inch rectangle, and spread the filling evenly, leaving a small margin at the top edge. Roll the dough tightly into a log, cut it into pieces about 1 ¾ inch wide, and place the discs in a baking pan with space between them.
Cover the pan of shaped rolls and let them proof in a warm place (around 77 °F/25 °C) for two to three hours, until the rolls are soft, light, and have puffed noticeably.
Preheat the oven to 400 °F (200 °C). Bake the proofed rolls for 20‑25 minutes, until they are well‑colored. While the rolls cool slightly, whisk together cream cheese, powdered sugar, whole milk, and vanilla extract to form a smooth glaze. Drizzle the glaze over the cooled rolls and serve.