Start by browning a total of 15 tablespoons of butter. Since you'll need a total of 12 tablespoons of browned butter for both the dough, filling, and frosting (some butter will evaporate during browning), browning extra ensures you have enough. Once browned, measure out what you need for the dough and filling (melted), and place the rest in a container to chill in the fridge overnight for the frosting. I always recommend browning all the butter at once for consistent flavor throughout the rolls.
In the bowl of an electric mixer, dissolve the instant dry yeast in the warm water and let it sit for 5 minutes. Once dissolved, add granulated sugar, 2 tablespoons melted browned butter (from Step 1), egg, milk powder, salt, and pumpkin puree, mixing until everything is well combined and there are no traces of egg yolk left. Add in 3 1/4 cups of flour and pumpkin pie spice, mixing until mostly combined. Attach the dough hook (if using a mixer) and knead, adding up to 1/2 cup extra flour a little at a time if the dough is too sticky. The dough should be soft and moist but not overly sticky. Continue kneading for about 8 minutes. Scrape the sides of the bowl as needed. You may also knead by hand on a floured surface if desired.
Lightly oil a large bowl and move the kneaded dough from Step 2 into it, turning it to coat in oil. Cover the bowl with a clean kitchen towel. To create a warm environment for rising, preheat the oven to 200°F (93°C), then turn the oven off and place the bowl inside. Let the dough rise for 45 minutes to 1 hour, or until doubled in size. While the dough rises, prepare the filling by mixing brown sugar, pumpkin pie spice, and ground cinnamon together in a small bowl. I like to mix the filling ingredients while waiting for the dough – it saves time and infuses the sugar mixture with spice.
Once the dough from Step 3 has doubled in size, punch it down with clean hands to release air bubbles. On a floured work surface, roll the dough out into a 16-inch by 14-inch rectangle. Brush 4 tablespoons of melted browned butter (from Step 1) over the dough surface. Evenly sprinkle the prepared sugar-spice filling (from Step 3) over the buttered dough. Roll the dough tightly into a log. For even rolls, score the log into 12 pieces before slicing with unflavored dental floss or a serrated knife. Place the rolls into a greased 9"x13" baking dish, cover with plastic wrap, and let rise overnight in the fridge or for about 30 minutes at room temperature until doubled in size.
If refrigerated overnight, let the unbaked cinnamon rolls sit at room temperature for about 45 minutes to rise and come to room temperature. Preheat the oven to 350°F (180°C). Bake the rolls for 22–27 minutes, or until golden brown. For extra precision, you can use a digital thermometer to check for doneness—the internal temperature should reach 190°F (88°C). Allow the finished rolls to cool for 5–10 minutes before frosting. I always let my rolls cool just a little so the icing partially soaks in and partially stays thick on top.
While the cinnamon rolls bake, prepare the frosting. In the bowl of an electric mixer, beat cream cheese and 1/4 cup softened browned butter (from Step 1, softened to room temperature) together for 2 minutes, scraping the bowl as needed, until light and fluffy. Add the vanilla extract, heavy cream, and confectioners’ sugar. Beat on low speed until combined, then increase to high speed and beat for about 4 minutes, until the frosting is fluffy and smooth. I sometimes use a splash more cream to make the frosting extra spreadable!
Spread the prepared brown butter cream cheese frosting (from Step 6) onto the warm cinnamon rolls (from Step 5). Let the frosting melt slightly into the rolls, then serve immediately for the best taste and texture. Store any leftovers in an airtight container for up to 3 days, though they are best enjoyed fresh.