Preheat oven to 320°F (160°C/Gas Mark 3).
Warm milk until just lukewarm, then stir in yeast and granulated sugar. Leave for 10 minutes until foamy.
Add melted butter and eggs, whisking gently until smooth.
Gradually mix in flour to form a dough.
Knead lightly on a floured surface for 2–3 minutes. Return to bowl, cover, and let rise in a warm place for 30 minutes.
Roll dough into a rectangle. Spread pumpkin purée evenly over the surface.
Mix brown sugar, cinnamon, and nutmeg, then sprinkle across the dough.
Roll into a log and cut into 1-inch slices.
Line a 13x9 inch baking pan with parchment paper and arrange rolls inside. Bake for 20 minutes, or until golden brown.
While baking, whisk cream cheese, powdered sugar, pumpkin purée, and milk until smooth. Add a splash of water if needed to thin.
Spread frosting over warm rolls, let set for 5–10 minutes, and sprinkle with cinnamon. Serve and enjoy!