In a small saucepan over medium heat, melt 15 tablespoons of butter, swirling occasionally. Cook until the butter turns golden brown and smells nutty, about 5-7 minutes. Pour into a heatproof bowl and let cool. Use 2 tablespoons for the dough, 6 tablespoons for the filling, and reserve the remaining for the frosting; chill the frosting portion until firm, then bring to room temperature before using.

In the bowl of a stand mixer, dissolve the yeast in warm water and let sit for 5 minutes until foamy. Add the sugar, 2 tablespoons melted brown butter, egg, milk powder, salt, and pumpkin puree. Mix until smooth and no traces of egg remain.

Add 3 1/4 cups of flour and the pumpkin pie spice. Mix on low until combined, then switch to the dough hook. If the dough is very sticky, add up to 1/2 cup more flour, 1/4 cup at a time, until it forms a soft, moist ball that pulls away from the bowl. Knead on medium speed for 8 minutes, scraping the bowl occasionally. Alternatively, knead by hand on a floured surface.

Preheat the oven to 200°F, then turn it off to create a warm environment. Lightly oil a large bowl, place the dough inside, and turn to coat. Cover with a clean kitchen towel and let rise in the warm oven for 45-60 minutes, until doubled in size.

Punch down the risen dough to release air. On a floured surface, roll it into a 16x14-inch rectangle. Brush the surface with the 6 tablespoons of melted brown butter. In a small bowl, mix the brown sugar, cinnamon, and pumpkin pie spice, then sprinkle evenly over the butter.

Starting from the long side, tightly roll the dough into a log. Use a serrated knife or unflavored dental floss to slice into 12 even rolls. Arrange the rolls in a greased 9x13-inch baking dish. Cover with plastic wrap and refrigerate overnight, or let rise at room temperature for about 30 minutes until doubled.

In the morning, remove the rolls from the fridge and let them sit at room temperature for 45 minutes to warm up. Preheat the oven to 350°F. Bake for 22-27 minutes, until golden and the internal temperature reaches 190°F. Let cool for 5-10 minutes before frosting.

While the rolls bake, in a stand mixer with the paddle attachment, beat the cream cheese and room-temperature brown butter on medium speed for 2 minutes until light and fluffy. Scrape down the bowl.

Add the vanilla extract, heavy cream, and confectioners' sugar. Mix on low until combined, then beat on high for 4 minutes until smooth and creamy. Spread the frosting over the warm rolls so it melts into each roll.

Store leftover rolls in an airtight container at room temperature for up to 3 days, though they are best enjoyed fresh.