Add the all-purpose flour, yeast, brown and white sugar, and pumpkin pie spice mix to the bowl of a stand mixer. Mix it all together so that things are well-combined.

In a microwave safe bowl, heat the buttermilk, pumpkin puree,
butter, and oil for 1 minute. Whisk it all together until well-combined.

Fold the warm pumpkin mixture into the dry ingredients and
add the egg. On low speed, knead the dough for 5-7 minutes. If the dough looks too soft, and things haven't combined well enough, add up to ½ cup of additional flour. The dough will be pretty shaggy, and this is okay. Just make sure that there are no pockets of flour hiding under the ball of dough, especially at the bottom of the bowl. Mix those in with a spatula.

Scoop the dough out onto a piece of parchment paper. Spray the bowl of the stand mixer with cooking spray. Return the
ball of dough to the now lubricated bowl. Cover the bowl with plastic wrap, and cover the plastic wrap with a clean kitchen towel.

Put the bowl in a warm, draft-free place, and let it rise until doubled in size (about 2 hours).

When the dough is nearly done rising, line a 9x13-inch pan
with parchment paper, spray it with cooking spray, and set it aside. Alternatively, spray two 9-inch round cake pans, and set aside.

Mix all of the filling ingredients in a small bowl. Set aside.

Melt the butter in another bowl. Set aside.

Once it has risen, turn the dough out onto a floured surface. I used a silicone baking sheet with a little bit of flour. Knead it lightly for about 1 minute.

Using a rolling pin, roll the dough into a 12x10-inch rectangle. Drizzle the melted butter evenly over the dough, and use a pastry brush to help spread it around. Sprinkle the filling over the dough in an even layer.

Starting on one of the long edges, roll the dough into a
long cylinder, as tightly as possible.

Using a sharp knife, or a bench scraper, cut the cylinder of dough into 12 evenly-sized rolls.

Place the 12 rolls into the prepared pan(s). Cover the pan(s) with plastic wrap and let it rest in a warm, draft-free place for about an hour. The rolls should approximately double in size.

Preheat the oven to 350 degrees F. Bake the rolls for 20-25 minutes, or until golden brown and set.

Allow the rolls to cool in the pan a bit before serving.  If you're
going to frost them, you should frost the rolls while they're still pretty warm.

Cream the cream cheese, butter, maple syrup, and vanilla extract together until smooth.

Add 1 cup of the powdered sugar and beat until combined. Add as much of the 2nd cup of powdered sugar as you'd like, until the icing reaches the desired consistency.

Slather the rolls with the icing.