In the evening, make the dough. In a stand mixer bowl, whisk together the milk, melted butter, egg, sourdough starter, and granulated sugar. Add the flour and salt. Using the paddle attachment, mix on low until a shaggy dough forms. Cover and let rest for 30 minutes.
Switch to the dough hook and knead on medium-low speed for 6 to 8 minutes, until the dough is smooth and pulls away from the sides of the bowl. Transfer the dough to a lightly oiled bowl, cover it, and let it rise at room temperature overnight, or for 8 to 12 hours, until doubled in size.
The next morning, prepare the filling by mixing the softened butter, sugar, cinnamon, and flour in a small bowl until it forms a paste. Lightly flour a work surface and roll the dough into a 16x12-inch (40x30 cm) rectangle.
Spread the filling evenly over the dough, leaving a 1/2-inch (1 cm) border on one of the long edges. Starting from the other long edge, roll the dough into a tight log. The seam should be facing down.
Cut the log into 8 equal-sized rolls using a sharp knife or unflavored dental floss. Arrange the rolls cut-side up in a greased 9-inch round baking pan. Cover the pan and let the rolls rest in a warm spot for 1 to 2 hours, until they look puffy.
Preheat your oven to 350°F (175°C). Bake the rolls for 30 to 35 minutes, or until they are golden brown and cooked through. Let them cool in the pan for 15 minutes before transferring to a wire rack.
While the rolls cool, make the glaze. In a medium bowl, beat the softened cream cheese and butter until smooth. Gradually beat in the powdered sugar, then add milk one tablespoon at a time until you reach a smooth, spreadable consistency.
Spread the glaze over the warm cinnamon rolls before serving.