Pour the warm milk into a large bowl. Stir in the yeast and a teaspoon of the sugar. Let stand for 5–10 minutes, until foamy.
Add the remaining sugar, pumpkin puree, egg, melted butter, and vanilla. Mix until combined.
Gradually add the flour, salt, cinnamon, and pumpkin pie spice. Mix until a soft dough forms.
Transfer the dough to a lightly floured surface and knead for 6–8 minutes, until smooth and elastic.
Place the dough in a lightly greased bowl. Cover and let rise for about 1 hour, or until doubled in size.
For the filling, combine the brown sugar, cinnamon, pumpkin pie spice, and nutmeg in a small bowl.
Roll the risen dough into approximately a 15x10-inch rectangle.
Spread the softened butter evenly over the dough, then sprinkle the cinnamon-sugar mixture over the top.
Starting from the long side, tightly roll the dough into a log.
Cut into 12 equal rolls and arrange them in a greased 9x13-inch baking dish.
Cover and let rise for another 30–40 minutes.
Preheat the oven to 350°F (175°C).
Bake for 22–28 minutes, or until lightly golden and cooked through.
Beat the cream cheese and butter until smooth. Add powdered sugar and vanilla, then gradually add milk until the glaze reaches your desired consistency.
Spread the cream cheese glaze over the warm cinnamon rolls and serve.