Heat the oven to 350°F and line baking sheets with parchment.
Whisk the flour, baking soda, cinnamon, and salt in a medium bowl.
Beat the butter and sugars until light and fluffy. Beat in the egg, pumpkin, and vanilla.
Mix in the dry ingredients just until combined, then fold in the oats.
Drop rounded tablespoons of dough onto the prepared sheets, leaving room to spread.
Bake for 10 to 12 minutes, until the centers are set. Cool completely.
Beat the creme butter, powdered sugar, vanilla, and heavy cream until smooth and fluffy.
Spread creme on the flat side of half the cookies and top with the remaining cookies.