Bloom the yeast: In the bowl of a stand mixer, whisk the warm milk with a pinch of the granulated sugar and the yeast. Let it sit 5–10 minutes until foamy. If it never foams, the milk was too hot or the yeast is dead — start over.

Make the dough: Add the remaining sugar, pumpkin puree, egg, egg yolk, melted butter, and vanilla to the yeast mixture and whisk to combine. In a separate bowl, whisk the flour, salt, cinnamon, ginger, and nutmeg. Add the dry ingredients to the wet and mix with the dough hook until a shaggy dough forms. Knead on medium speed for 6–8 minutes until smooth and elastic — the dough will be soft and slightly tacky, but should not stick to your fingers. Resist adding too much flour.

First rise: Transfer the dough to a greased bowl, cover, and let rise in a warm spot for 1 to 1 1/2 hours, until doubled in size.

Shape: Punch the dough down and roll it into a 16 x 12-inch (40 x 30-cm) rectangle on a lightly floured surface. Spread the very soft butter evenly over the dough, leaving a 1/2-inch border along the far long edge. Stir the brown sugar, cinnamon, nutmeg, and salt together and sprinkle evenly over the butter. Press lightly so it adheres.

Roll and slice: Starting from the long edge nearest you, roll the dough into a tight log, pinching the seam to seal. Use unflavored dental floss or a sharp serrated knife to cut 12 equal rolls. (Floss gives the cleanest swirls — slide it under the log, cross the ends, and pull.)

Second rise: Arrange the rolls cut-side up in a buttered 9 x 13-inch baking dish. Cover and let rise 45–60 minutes, until puffy and nearly touching.

Bake: Preheat the oven to 350°F (175°C). Bake 22–25 minutes, until golden on top and the centers spring back when lightly pressed. A thermometer should read about 190°F (88°C) in the center of a middle roll.

Frost: While the rolls bake, beat the cream cheese, butter, powdered sugar, maple syrup, vanilla, and salt until completely smooth. Spread generously over the warm rolls so it melts into every swirl. Serve warm.