In a large mixing bowl, combine all-purpose flour, instant yeast, and salt. Warm the milk until slightly hot to the touch, then whisk it with the pumpkin puree, egg, and softened butter until smooth. Gradually mix this wet ingredient combination into the dry ingredients, stirring until a soft dough forms, which should take about 2-3 minutes of mixing.

Knead the dough on a floured surface for about 5-7 minutes until it becomes smooth and elastic. Place the dough in a lightly greased bowl, covering it with a clean kitchen towel. Let it rise in a warm, draft-free area for about 1 hour or until it doubles in size.

Once the dough has risen, prepare the filling by squeezing excess moisture from the pumpkin puree. In a mixing bowl, combine the drained pumpkin with brown sugar, ground cinnamon, and pumpkin pie spice. Mix well until all ingredients are evenly blended.

Lightly flour a clean surface and roll the dough into a rectangle, approximately 12x18 inches in size. Spread the prepared filling evenly across the dough, leaving a half-inch border. Starting from one long side, tightly roll the dough into a log.

Using a sharp knife or clean dental floss, slice the log into 12 equal pieces. Arrange the rolls in a greased 9x13 baking dish, placing them close together but not touching. Cover with a towel and let them rise again in a warm place until puffy.

Preheat your oven to 350°F (175°C). Once the rolls have risen, place them in the oven and bake for approximately 20-25 minutes until they are golden brown and fragrant.

After allowing the rolls to cool for 10-15 minutes, prepare the cream cheese frosting. In a bowl, mix room temperature cream cheese with vanilla bean paste until fluffy. Spread the frosting generously over the warm rolls.