Butter one 10-inch round cake pan, line the bottom with parchment paper, and butter the parchment.

For the Pumpkin Dough: Sprinkle yeast over milk in bowl of stand mixer fitted with dough hook. If using instant yeast, proceed with recipe, if using active dry yeast let mixture stand 5 to 10 minutes or until foamy. While waiting, whisk together 3½ cups flour, granulated sugar, salt, cinnamon, ginger, and cardamom in a separate bowl.

Whisk together remaining dough ingredients with yeast mixture. Add flour mixture and begin mixing on low until flour is incorporated. Increase speed to medium and knead until slightly sticky but soft, adding additional ½ cup flour if needed (dough will not pull away from sides of bowl, but will be tight and glutenous.)

Remove the dough from the bowl, carefully form it into large ball, smooth the top with your hands, and place it in a clean, lightly greased bowl. Cover with plastic wrap and let the dough rest for 60 minutes until doubled in size.

For the Filling: In a small bowl, stir together the brown sugar, spices, and salt.

Assemble the Rolls: Dust a work surface with a sprinkling of flour. Using a rolling pin, roll the dough into a large rectangle approximately 20 by 10 inches, spread on softened butter, and sprinkle the filling over the butter, leaving a ¼-inch border around the edges. Use the palms of your hands to press the filling lightly into the dough.

Roll up the long side of the rectangle to form a tight log and place it seam side down. Slice the log into ten 2-inch rolls. Place one roll in the center of the cake pan, then fill in the rest of the pan with the other rolls (alternately cut log into 12 and place evenly in 9 by 13-inch pan). Brush the tops of the rolls with melted butter (if desired) or spray with nonstick spray, cover with plastic wrap, and set aside until the rolls have almost doubled in size, about 45 minutes.

If you’re doing this the day before, you can skip the second rise in the pan and put them in the fridge overnight. In the morning, leave them out for an hour or two to warm up and finish rising.

Preheat the oven to 350°F and position the oven rack in the center.

Bake for 25 to 30 minutes or until the tops of the rolls are browned. In order to pour your icing over still-warm rolls, prep all the frosting ingredients while the rolls are baking and put together the frosting (this will only take about 5 minutes) immediately after the rolls come out of the oven.

Make the Frosting: In the bowl of a standing mixer fitted with the paddle attachment, beat the cream cheese and milk on medium speed until the mixture is lump-free. Add the confectioners’ sugar and vanilla, if using, and beat on medium-low speed until a smooth, fluid mixture forms.

Serve the Rolls: Invert the pan of rolls onto a serving plate or leave them in the pan for a rustic look. Pour the frosting over the warm rolls. It’s okay if a little bit of the frosting drips down the sides- it’s even encouraged. (Alternatively, use an offset spatula to apply the icing.) Serve immediately.