01 - Combine warm milk, active dry yeast, and granulated sugar in a large mixing bowl. Allow to rest for 5 to 10 minutes until the mixture turns foamy.
02 - Incorporate pumpkin puree, melted butter, egg, and salt into the yeast mixture. Blend until thoroughly combined.
03 - Gradually add all-purpose flour to the bowl, mixing until a soft dough forms. Knead the dough on a lightly floured surface for 5 to 7 minutes until smooth and elastic.
04 - Transfer the dough to a greased bowl, cover with plastic wrap or a towel, and let rise for approximately 1 hour or until doubled in size.
05 - Roll the proofed dough into a 10 by 14-inch rectangle. Evenly spread softened butter and pumpkin butter across the surface.
06 - Sprinkle the dough evenly with brown sugar and ground cinnamon.
07 - Roll up the dough tightly from the long side. Slice into 9 to 12 equal pieces using a sharp knife or dental floss.
08 - Arrange the rolls in a greased baking dish, cover, and allow to rise for 30 to 45 minutes until puffy.
09 - Preheat the oven to 350°F (175°C). Bake the rolls for 20 to 25 minutes, or until the tops are golden brown and the centers are cooked through.
10 - While the rolls bake, heat brown sugar, butter, and milk in a small saucepan over medium heat, stirring until the sugar has dissolved. Remove from heat, mix in vanilla extract, then gradually whisk in powdered sugar until the frosting is smooth.
11 - Spread the warm frosting generously over baked rolls. Serve immediately while still warm.