Prepare the oven: Heat the oven to 350°F and line baking sheets with parchment paper.
Blot the pumpkin: Press the pumpkin puree between paper towels or a clean dish towel until excess moisture is removed.
Mix the dry ingredients: Whisk the flour, cinnamon, ginger, nutmeg, cloves, baking soda, and salt in a medium bowl.
Cream the butter and sugars: Beat the softened butter, brown sugar, and granulated sugar until creamy.
Combine the wet ingredients: Beat in the pumpkin, molasses, vanilla, and egg yolk.
Finish the dough: Mix in the dry ingredients, then stir in the oats until evenly combined.
Bake the cookies: Scoop 1 to 1 1/2 tablespoons of dough per cookie, spacing them 2 inches apart. Bake for 7 to 10 minutes, until the tops look set.
Cool completely: Leave the cookies on the baking sheets for 10 minutes, then transfer them to a wire rack.
Make the filling: Beat the butter and cream cheese until smooth. Add the powdered sugar, vanilla, and salt, mixing until creamy. Add milk or cream if needed.
Assemble: Spread 1 to 1 1/2 tablespoons of filling on the bottom of one cookie and top with another cookie.