Warm the milk until just slightly hot (not boiling) and stir in the sugar and yeast. Let sit for 5–10 minutes until foamy.
In a large bowl, whisk together pumpkin, egg, and melted butter. Add the foamy yeast mixture and stir.
Add flour, salt, and cinnamon. Mix with a spoon or spatula until dough comes together, then knead by hand (or dough hook) for 6–8 minutes until smooth.
Cover and let rise in a warm spot for 1 hour or until doubled in size.
Roll dough into a large rectangle on a floured surface. Spread softened butter over the top, then mix and sprinkle the filling evenly.
Roll up tightly from the long side and slice into 12 pieces. Place in a greased 9x13 pan.
Cover and let rise again for 30–40 minutes while the oven preheats to 350°F.
Bake for 22–26 minutes until golden and the centers are cooked through.
While rolls are warm, whisk together glaze ingredients until smooth and pour over the top.