Warm the milk and activate the yeast in it, then stir in the sugar, melted butter, pumpkin puree, and eggs until smooth. Let it sit until foamy for a clear, active yeast start.

Mix in the flour, pumpkin pie spice, and salt, then knead until the dough is smooth and elastic, about 8 minutes. If using a stand mixer, keep the dough moving continuously for even gluten development.

Cover the dough and let it rise for 1 hour at room temperature (or until doubled in size). The dough should look puffy with a noticeably increased volume.

Roll the dough into a 12x18 inch rectangle, pressing out any thick seams so it rolls evenly. Aim for a uniform thickness so the swirl bakes consistently.

Spread the softened butter over the dough, then sprinkle with brown sugar, cinnamon, and pumpkin pie spice. Leave a small border so the filling stays inside as you roll.

Roll the dough up tightly from one long edge to the other to form a log. Tight rolling helps keep the cinnamon swirl defined in each roll.

Cut the log into 12 rolls and place them in a baking dish or on a sheet pan. Keep the cut sides up so the centers rise well.

Cover and let the rolls rise for 45 minutes until visibly puffed. They should feel lighter and look taller even before baking.

Bake at 375°F for 22 to 25 minutes, until the tops are lightly golden. The finished rolls should look set and spring back gently.

Beat the cream cheese and butter smooth, then mix in the maple syrup, strong coffee, and powdered sugar until glossy. Drizzle the frosting over warm rolls for the best melt and shine, using a quick back-and-forth motion.