Brown the butter – In a saucepan, melt all the butter (¾ cup total) you’ll need (for dough, filling, and frosting). Cook on medium heat, swirling, until golden brown with nutty aroma. Transfer to a bowl to cool.
Activate the yeast – Warm milk to 100–110°F (microwave in 20-second bursts). Stir in yeast and let sit 5–10 minutes until bubbly.
Make the dough – In a large bowl, whisk together the yeast mixture, brown sugar, pumpkin puree, ¼ cup brown butter, eggs, and vanilla. Add flour and salt. Mix until combined, then knead 8–10 minutes (stand mixer or by hand) until smooth and elastic.
First rise – Place dough in a greased bowl, cover, and let rise 60–90 minutes or until doubled in size.
Prepare filling – Mix brown sugar, cinnamon, and pumpkin pie spice in a small bowl.
Shape rolls – Roll risen dough on a floured surface into a 12×18 inch rectangle. Spread ¼ cup brown butter edge-to-edge, sprinkle sugar-spice mixture, and rub it in with your hands. Slice into 12 strips, roll each up, and place into a greased 9×13 pan. Sprinkle 2 tbsp brown sugar on the bottom if you want extra gooey rolls.
Second rise – Cover pan and let rise 30 minutes until puffy. Optional: pour ¼ cup heavy cream over rolls before baking for extra fluffiness.
Bake – Preheat oven to 350°F (175°C). Bake 20–25 minutes until golden brown on top but still soft in the center.
Make frosting – Beat cream cheese, 4 tbsp brown butter, and maple syrup until smooth. Gradually add powdered sugar (2–2 ½ cups) until fluffy.
Frost & serve – Spread frosting over warm rolls and enjoy immediately.
