Generously butter a 8" cake pan. Crumple up some parchment paper, then un-crumple it and place it into the buttered cake pan, making sure it sticks to the bottom and sides. Set aside.
In a small bowl, combine the brown sugar and pumpkin pie spice and set it aside.
Once the dough has finished rising, lightly punch it down to remove any excess air in it. Transfer the dough to a clean and lightly floured surface, then roll it out to a 12″ x 16″ (30 x 40 cm) rectangle.
Melt the butter, then mix it in with the spiced sugar and spread it over the dough.
From the longer side, cut the dough into 6 two inch strips.
Roll up one of the strips as you would with a standard cinnamon roll and place it into the center of your prepared pan.
Pick up another strip of dough and coil it around the center cinnamon roll. Repeat until you have used up all six strips of dough.
Lightly cover the pan with a towel, and let the cake rise in a warm environment until doubled in size (~30 minutes).
Preheat the oven to 350°F / 175°C.
(Optional, for browning) Make an egg wash by whisking together an egg with 1 tbsp. milk, then brush it over the cake.
Bake for 25-30 minutes, until the top of the cake is golden brown and the internal temperature of the cake has reached 180°F / 82°C