1. 1. Prepare the Dough Base: In a large mixing bowl, combine the warm milk, unfed sourdough starter, granulated sugar, salt, egg, and pumpkin puree. Whisk until well combined. Gradually add the flour, one cup at a time, mixing until a shaggy dough forms. Pour in the melted butter and continue to mix until the butter is fully incorporated and the dough comes together. It will be a soft, slightly sticky dough.

2. 2. Knead and First Rise: Turn the dough out onto a lightly floured surface. Knead for 5-7 minutes until the dough is smooth and elastic. Place the dough in a lightly oiled bowl, turning once to coat. Cover the bowl with plastic wrap or a clean kitchen towel and let it rise in a warm place for 1 hour 30 minutes, or until it has roughly doubled in size. The dough should feel soft and puffy when gently pressed.

3. 3. Roll Out the Dough: Once risen, gently punch down the dough to release the air. Turn it out onto a lightly floured surface. Using a rolling pin, roll the dough into a large rectangle, approximately 18×12 inches. Aim for an even thickness across the entire rectangle.

4. 4. Spread the Filling: In a small bowl, cream together the softened butter, brown sugar, ground cinnamon, and pumpkin pie spice until well combined and spreadable. Evenly spread this delicious filling over the entire surface of the rolled-out dough, leaving a small border (about 1/2 inch) along one of the longer edges.

5. 5. Roll and Slice: Starting from the long edge opposite the border, tightly roll the dough into a log. Once rolled, use a sharp knife or unflavored dental floss to slice the log into 12 even rolls, each about 1.5 inches thick. A good trick for even slicing is to gently mark the log into 12 sections before cutting.

6. 6. Second Rise and Bake: Arrange the sliced rolls in a lightly greased 9×13 inch baking dish, leaving a little space between each roll as they will expand. Cover the dish loosely with plastic wrap or a kitchen towel and let them rise again in a warm spot for 30 minutes, or until visibly puffy. Preheat your oven to 375 F (190 C). Bake for 25-30 minutes, or until the rolls are golden brown and cooked through. The center of the rolls should feel set when gently pressed.

7. 7. Prepare the Frosting and Finish: While the rolls are baking or cooling slightly, prepare the coffee maple frosting. In a medium bowl, beat the softened cream cheese and butter together until smooth and creamy. Gradually add the powdered sugar, beating until fully incorporated. Stir in the cooled brewed coffee, maple syrup, and vanilla extract. Beat until the frosting is light and fluffy. Once the rolls are out of the oven, let them cool for about 5-10 minutes before generously spreading the frosting over the warm rolls. This allows the frosting to melt slightly and seep into all the gooey crevices.