Warm the milk until lukewarm (not hot) and combine it with the dry yeast and granulated sugar in a small bowl. Stir gently and let it sit for 10 minutes in a warm spot until bubbly and frothy.
In a large mixing bowl, add the melted butter, eggs, and the proofed yeast mixture. Stir gently with a whisk until smooth.
Gradually add the flour, cinnamon, nutmeg, and brown sugar to the wet ingredients. Mix until a dough begins to form.
Transfer the dough onto a floured surface and knead for 2–3 minutes until soft and pliable. Place the dough back into the bowl, cover with a clean towel, and let it rise in a warm place for 30 minutes.
Once the dough has doubled in size, roll it out on a floured surface into a rectangular shape. Spread the pumpkin puree evenly over the dough.
In a small bowl, mix the brown sugar, cinnamon, and nutmeg. Sprinkle the mixture evenly over the pumpkin layer.
Carefully roll the dough into a log, starting from one long side. Slice into 1-inch thick rolls using a sharp knife or dental floss for clean cuts.
Line a 13×9-inch pan with parchment paper and arrange the rolls with a bit of space between them. Bake in a preheated oven at 320°F for 20 minutes or until golden brown.
In a small bowl, whisk the cream cheese, powdered sugar, pumpkin puree, and milk until smooth. Adjust consistency with a splash of water if needed.
Spread the frosting over the warm rolls and let it set for 5–10 minutes. Sprinkle a pinch of cinnamon on top for garnish. Serve warm and enjoy!