1. 1. Prepare the Dough Base: In a large mixing bowl, combine the sourdough discard, pumpkin puree, granulated sugar, melted butter, and egg. Whisk these wet ingredients together until they are well combined and smooth. The mixture should have a slightly thick, creamy consistency.

2. 2. Combine Dry Ingredients: In a separate medium bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and pumpkin pie spice. Make sure there are no lumps and the spices are evenly distributed throughout the flour.

3. 3. Form the Dough: Gradually add the dry ingredient mixture to the wet ingredients, mixing with a spoon or spatula until a soft, shaggy dough forms. Once most of the flour is incorporated, turn the dough out onto a lightly floured surface and knead gently for about 2-3 minutes until it comes together into a cohesive, slightly tacky ball. Avoid over-kneading, as this can make the rolls tough.

4. 4. Shape the Rolls: Roll the dough into a large rectangle, approximately 12×18 inches, on your lightly floured surface. The dough should be about 1/4 inch thick. In a small bowl, mix the softened butter with the packed brown sugar and an additional teaspoon of ground cinnamon until it forms a thick paste. Evenly spread this cinnamon-sugar mixture over the entire surface of the dough rectangle, leaving a small border along one of the long edges.

5. 5. Roll and Slice: Starting from the long edge opposite the border, carefully roll the dough tightly into a log. Once rolled, use a sharp knife or unflavored dental floss to cut the log into 12 even slices, each about 1 1/2 inches thick.

6. 6. Bake the Rolls: Arrange the sliced rolls cut-side up in a lightly greased 9×13 inch baking dish. Leave a little space between them as they will expand during baking. Bake in a preheated oven at 375 F (190 C) for 25-30 minutes, or until the rolls are golden brown on top and cooked through in the center. The internal temperature should reach around 200 F if you use a thermometer.

7. 7. Prepare the Icing: While the rolls are baking, prepare the icing. In a medium bowl, whisk together the powdered sugar, milk or cream, and vanilla extract until smooth and creamy. If the icing is too thick, add a tiny bit more milk; if it’s too thin, add a little more powdered sugar.

8. 8. Finish and Serve: Once the rolls are out of the oven, let them cool in the baking dish for about 5-10 minutes. Then, generously drizzle or spread the prepared icing over the warm rolls. Serve immediately and enjoy!