In a medium bowl, combine the all-purpose flour, pumpkin pie spice blend, salt, baking powder, and baking soda. Set aside.
In a large mixing bowl, using a handheld mixer on low speed, beat together the unsalted butter and cream cheese for 1 to 2 minutes or until no lumps remain.
Add granulated sugar, pure pumpkin puree, and vanilla extract to the butter and cream cheese mixture. Beat for an additional 1 to 2 minutes or until the dough comes together to form a rough ball.
Add the reserved flour mixture to the bowl of wet ingredients. Mix together just until all the dry ingredients are fully incorporated. Do not overmix, or your dough will be tough.
Turn out your dough onto a lightly floured surface (a piece of parchment paper works great). Form your dough into a rough rectangle and roll it out to a 10x12-inch rectangle that is approximately ¼-inch thick.
In a small bowl, stir together the melted and cooled unsalted butter, light brown sugar, and pumpkin pie spice blend to create the filling layer.
Spread the sugar and spice blend evenly over the dough.
Slowly roll the dough, using your fingertips, into a log. You will want to roll from the longer end of the dough, being careful to pinch together any dough that may lightly split open as you roll.
Wrap your cookie dough log with plastic wrap and place it in the refrigerator to chill. When wrapping your cookie dough log, try not to flatten the shape as much as possible. You want to make sure that when you slice your cookies, they are a circle.
Chill your pumpkin spice roll cookie dough log for 2 hours or up to 2 days before slicing and baking.
Preheat the oven to 350°F. Line a baking sheet with parchment paper.
Slice the chilled cookie dough log into ½ to ¾-inch thick slices. You should get between 16 to 18 cookies. You can trim off the very edges of the log so that you have evenly shaped and sized cookies.
Place 5 to 6 cookies onto each prepared cookie sheet. You need to allow space between the cookies because they will spread some as they bake.
Bake for 12 to 14 minutes or until just barely golden on the edges. Repeat until all the cookies have been baked.
Allow your cookies to cool on the baking sheet for 2 to 3 minutes before transferring them to a cooling rack.
While your cookies cool completely on the counter, you can make your icing drizzle by whisking together, in a medium bowl, the sifted powdered sugar, milk, vanilla extract, and melted and cooled unsalted butter until you have a smooth mixture. You should be able to use a spoon to drizzle the icing over the cooled cookies. If your icing is too thick, then you can thin it with a little more milk, starting with ½ teaspoon at a time until you reach the desired consistency. If it is too thin, you can add a little powdered sugar, 1 tablespoon at a time, to reach the desired consistency.
Transfer the icing to a piping bag or zip-top plastic bag, and drizzle the icing over the pumpkin spice cinnamon roll cookies once they have cooled completely. Allow the icing on the cookies to dry and harden before placing them into a storage container.