Preheat the oven to 375ºF. Line 3 baking sheets with parchment paper or a silicone mat. Set aside.

Take 4 connected sheets of paper towels and fold it in half. Lay the folded paper towels across a baking sheet or large plate. Spread the pumpkin puree in an even layer over the paper towels and set aside.

In a large mixing bowl, beat together the butter and sugars together until light and fluffy. Add the egg yolk and molasses and beat until combined.

Lift one of the shorter sides of the paper towel slightly and gently scrape the pumpkin puree loose. Lift the edge of the paper towel a little higher and give it a gentle shake. The puree should begin to roll down the paper towel and form a log. Scrape loose as needed. Transfer the puree to the mixing bowl with the butter mixture and beat on low speed until well incorporated.

In a separate bowl, combine the flour, baking soda, cinnamon, ginger, and salt. Stir with a whisk. Add the flour mixture to the pumpkin mixture, beat on low speed just until combined. With a silicone spatula, gently stir in the oats.

Use a cookie scoop to drop 1 ½-tablespoon sized balls of dough, 2 inches apart, onto the prepared baking sheet. Bake for 10 to 12 minutes. Allow the cookies to cool on the pan for 10 minutes; transfer to a wire rack to cool completely.

In the bowl of a stand mixer fitted with the paddle attachment or a large mixing bowl with a handheld electric mixer, beat the butter on medium-high speed until creamy and pale in color, about 5 minutes.

Add half the confectioners' sugar and beat on low speed just until the sugar has fully moistened, then turn the speed up to medium-high and beat until well incorporated, about 3-5 minutes.

Add the remaining confectioners' sugar and beat on low speed just until the sugar has fully moistened, then turn the speed up to medium-high and beat until well incorporated, about 3-5 minutes.

Add the caramel sauce and mix on medium speed until the caramel is well incorporated, about 3-5 minutes.

Pipe or spread the cream filling on the flat side of half of the cookies and put the remaining cookies on top.