Wake up the yeast. In a large bowl, whisk warm milk, yeast, and 1 tablespoon of the sugar. Let sit 5 to 10 minutes until foamy. If you are using instant yeast, the foam may be subtle. Proceed as long as the yeast is within date and smells pleasantly yeasty.
Mix the wet ingredients. Whisk in the remaining sugar (3 tablespoons), pumpkin puree, egg, egg yolk, melted butter, and vanilla until smooth.
Add dry ingredients and form the dough. Add flour, salt, cinnamon, ginger, and nutmeg. Stir with a spoon until a shaggy dough forms.
Knead. Knead by hand on a lightly floured surface for 8 to 10 minutes or in a stand mixer with a dough hook for 5 to 7 minutes. The dough should be smooth and slightly tacky but not sticky.
Quick note on pumpkin: Pumpkin puree moisture varies by brand and homemade batches. If the dough feels like wet paste and will not hold together, add flour 1 tablespoon at a time. If it feels dry or stiff, add milk 1 teaspoon at a time.
First rise. Place dough in a lightly greased bowl, cover, and let rise in a warm spot until doubled, about 60 to 90 minutes.
Make the filling. In a small bowl, mix brown sugar, cinnamon, salt, and nutmeg (if using).
Prep the pan and roll out. Grease a 9x13-inch baking dish. Optional but handy: line with parchment with a little overhang for easy lift-out. Punch down the dough and roll it into a 16x12-inch rectangle on a lightly floured counter.
Fill. Spread the softened butter evenly over the dough, leaving a 1/2-inch clean border along the far long edge (the edge you will seal). Sprinkle the cinnamon sugar mixture over the butter and press lightly so it sticks.
Roll and slice. Starting from the long edge opposite the clean border, roll the dough into a snug log. Pinch the seam to seal. Slice into 12 equal rolls using a sharp knife or unflavored dental floss.
Yield: This makes 12 large, bakery-style rolls. If you want smaller rolls, slice into 15 and use a slightly larger pan or two pans.
Second rise. Arrange rolls in the prepared baking dish. Cover and let rise until puffy and touching, about 30 to 45 minutes. If your kitchen is cool, give it a little longer.
Overnight option: After arranging the rolls in the pan, cover tightly and refrigerate 8 to 12 hours. In the morning, let them sit at room temp until puffy, usually 45 to 90 minutes, then bake.
Bake. Heat oven to 350°F. Bake 22 to 28 minutes until the tops are light golden and the centers look set (not wet or doughy). For a temperature check, aim for about 185°F to 190°F in the center roll. If the tops brown too fast, tent loosely with foil for the last 8 to 10 minutes.
Make the icing. Beat cream cheese and butter until smooth. Add powdered sugar, vanilla, and a pinch of salt. Add milk 1 tablespoon at a time until you get a thick but spreadable icing.
Ice and serve. Let rolls cool 5 to 10 minutes, then spread icing over the warm rolls so it melts into the swirls. Serve immediately, ideally with coffee and zero plans.
