In a small bowl, whisk warm milk, yeast, and sugar. Let sit 5–10 minutes until foamy.

In a large bowl (or stand mixer), whisk together flour, salt, cinnamon, and nutmeg.

Add eggs, pumpkin puree, butter, and the yeast mixture. Mix until a shaggy dough forms.

Knead with a stand mixer (5–6 minutes) or by hand (8–10 minutes) until smooth and elastic. The dough will be slightly tacky but not sticky.

Place dough in a greased bowl, cover, and let rise in a warm place until doubled, about 1–1.5 hours.

In a medium bowl, mix softened butter, brown sugar, cinnamon, and pumpkin pie spice until a spreadable paste forms.

Once dough has risen, punch it down and roll out onto a lightly floured surface into a 12x18-inch rectangle.

Spread filling evenly over the dough.

Starting from the long side, roll dough tightly into a log. Slice into 12 even rolls.

Place rolls in a greased 9x13-inch pan. Cover and let rise again for 30–45 minutes, until puffy.

Preheat oven to 350°F (175°C).

Bake rolls for 25–30 minutes, until golden brown and centers are cooked through (cover with foil if tops brown too fast).

Beat cream cheese and butter until smooth. Add powdered sugar, vanilla, and milk (a little at a time) until creamy and spreadable.

Spread cream cheese icing over warm rolls and serve immediately.