Combine warm milk and yeast; let sit until foamy, about 5–10 minutes.
Whisk pumpkin puree, melted butter, sugar, and egg until smooth.
Stir in yeast mixture.
Add flour, cinnamon, and salt; mix into a shaggy dough.
Knead 6–8 minutes until smooth and elastic.
Place dough in a greased bowl, cover, and let rise 1–1.5 hours until doubled.
Roll dough into a 16x12-inch rectangle.
Spread softened butter over dough, leaving a border on one edge.
Mix brown sugar and spices; sprinkle evenly over butter.
Roll dough tightly into a log from the long edge; pinch seam to seal.
Slice into 12 rolls.
Arrange rolls in a greased 9x13-inch dish; cover and let rise 30–45 minutes.
Preheat oven to 350°F.
Bake 22–25 minutes until golden and cooked through.
Cool 10 minutes in the pan.
Beat cream cheese and butter until smooth; add powdered sugar and vanilla, then milk to reach spreadable consistency.
Spread frosting over warm rolls before serving.
