Preheat the oven to 375 degrees.  Lay a piece of parchment paper on a baking sheet.  Unroll the can of crescent roll dough.  If it is perforated, press the seams together to seal.  Cut diagonal strips on each side of the dough, leaving a solid strip in the center (where you will spread the filling).

Use a mixer to cream together the softened cream cheese, 2 Tbsp white sugar, and 1/2 tsp pumpkin pie spice.  Set aside.

In a small bowl, stir together 2/3 cup pumpkin puree, 1 Tbsp white sugar, and 1/2 tsp pumpkin pie spice.

Spread the cream cheese mixture down the center of the dough.  Then, spread the pumpkin mixture over the top of the cream cheese mixture.  Fold in the ends of the dough, then fold in the strips of dough to meet in the center.  

In a small bowl, combine 1 Tbsp turbinado sugar and 1/4 tsp pumpkin pie spice.  Sprinkle over the top before baking. 

Bake at 375 for 15 minutes.  While the braid is baking, in a mixer, cream together the ingredients for the glaze: cream cheese, milk, powdered sugar, and vanilla.  (Note that the vanilla will give it an off white color.  If you prefer a pure white color, leave the vanilla out.  I personally love the flavor of the vanilla glaze with the pumpkin pie spice).  

When the braid is finished baking, remove from the oven and drizzle with the glaze.  Let cool for a few minutes before slicing and serving.