Warm the liquid ingredients: In a small bowl, whisk the warm milk, pumpkin puree, egg, melted butter, and vanilla. The mixture should be lukewarm, not hot.

Mix the dry base: In a large bowl (or stand mixer bowl), combine 3 1/4 cups flour, yeast, sugar, salt, and pumpkin pie spice.

Form the dough: Pour the pumpkin mixture into the dry ingredients. Stir with a sturdy spoon until a shaggy dough forms. If very sticky, add more flour 1 tablespoon at a time.

Knead: Knead by hand on a lightly floured surface for 7–9 minutes, or in a stand mixer with a dough hook for 5–6 minutes, until smooth and slightly tacky. The dough should spring back when pressed.

First rise: Place the dough in a lightly oiled bowl, cover, and let rise in a warm spot until doubled, about 60–90 minutes.

Make the filling: Stir the softened butter, brown sugar, cinnamon, pumpkin pie spice, and salt into a spreadable paste.

Roll it out: Punch down the dough and roll into a 12x16-inch rectangle on a floured surface. Keep the edges neat for even rolls.

Spread and roll: Spread the filling evenly over the dough, leaving a 1/2-inch border on one long side. Roll up tightly from the opposite long side into a log.

Slice: Trim the ends, then cut into 12 even rolls. A piece of unflavored dental floss works well for clean cuts.

Second rise: Arrange rolls in a greased 9x13-inch pan. Cover and let rise until puffy, 30–45 minutes. They should nearly touch.

Bake: Preheat oven to 350°F (175°C). Bake 22–26 minutes, until the tops are lightly golden and the centers read about 190°F. Don’t overbake.

Make the glaze: Beat cream cheese and butter until smooth. Add powdered sugar, vanilla, salt, and enough milk to reach a pourable, creamy consistency.

Glaze and serve: Let rolls cool 10 minutes, then spread with glaze. Serve warm.