1. Prepare the Dough Base: In a large mixing bowl or the bowl of a stand mixer, combine the warm milk, active sourdough starter, granulated sugar, salt, egg, and pumpkin puree. Mix until well combined. Gradually add the all-purpose flour, one cup at a time, mixing until a shaggy dough forms.

2. Knead the Dough: Turn the dough out onto a lightly floured surface and knead for 5-7 minutes, or use a stand mixer with a dough hook for 3-5 minutes, until the dough is smooth and elastic. It should spring back when lightly poked.

3. First Rise: 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 2-3 hours, or until doubled in size. The dough should feel light and airy.

4. Roll and Fill: Once the dough has risen, gently punch it down and turn it out onto a lightly floured surface. Roll the dough into a large rectangle, approximately 18×12 inches. In a small bowl, combine the softened butter, brown sugar, cinnamon, nutmeg, and cloves for the filling. Spread this mixture evenly over the entire surface of the dough, leaving a small border along one long edge.

5. Shape the Rolls: 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 cut the log into 12 equal slices, about 1 1/2 inches thick.

6. Second Rise and Bake: Arrange the sliced rolls in a greased 9×13 inch baking dish. Cover loosely with plastic wrap or a kitchen towel and let them rise again in a warm spot for 30-45 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 internal temperature should be around 200 F (93 C).

7. Prepare the Frosting: While the rolls are baking, prepare the coffee maple frosting. In a medium bowl, beat together the softened cream cheese and butter until smooth and creamy. Gradually add the powdered sugar, mixing until fully incorporated. Stir in the cooled brewed coffee, maple syrup, and vanilla extract until the frosting is light and fluffy.

8. Frost and Serve: Once the cinnamon rolls are out of the oven, let them cool in the pan for about 5-10 minutes. Spread the generous amount of coffee maple frosting over the warm rolls. Serve immediately and enjoy the delightful flavors!