In a bowl, combine warm milk and yeast and let sit 5 minutes until foamy.
Mix pumpkin puree, sugar, melted butter, egg, salt, cinnamon, and nutmeg.
Add yeast mixture and gradually stir in flour until dough forms.
Knead dough 5–7 minutes until smooth.
Place dough in greased bowl, cover, and let rise 1 hour until doubled.
Roll dough into a rectangle.
Spread softened butter over dough and sprinkle brown sugar and cinnamon evenly.
Roll tightly into a log and slice into 12 rolls.
Place rolls in greased baking dish and let rise 20–30 minutes.
Bake at 350°F (175°C) for 20–25 minutes until golden.
Whisk glaze ingredients and drizzle over warm rolls.