In a large bowl, whisk together the sourdough starter, warm milk, pumpkin puree, sugar, egg, and melted butter until smooth.

Add the flour, salt, and cinnamon. Mix until a shaggy dough forms, then knead by hand or with a mixer for 8 to 10 minutes until soft, smooth, and slightly tacky. If needed, add a little more flour, 1 tablespoon at a time.

Place the dough in a lightly greased bowl, cover, and let rise at room temperature until puffy and nearly doubled, 6 to 10 hours depending on starter strength and room temperature.

For the filling, mix the brown sugar and cinnamon together in a small bowl.

Turn the dough out onto a lightly floured surface and roll into a rectangle about 12 x 16 inches. Spread the softened butter evenly over the surface, then sprinkle with the cinnamon-sugar mixture.

Starting from a long edge, roll the dough tightly into a log. Cut into 12 equal rolls and place them in a greased 9 x 13-inch baking dish.

Cover and let the rolls rise until noticeably puffy, 2 to 4 hours, or refrigerate overnight and bring to room temperature before baking.

Preheat the oven to 350°F (175°C). Bake the rolls for 25 to 30 minutes, until golden brown and cooked through.

While the rolls bake, beat together the cream cheese, powdered sugar, milk, and vanilla until smooth and spreadable.

Let the rolls cool for 10 minutes, then spread or drizzle with the cream cheese glaze and serve warm.