Preheat oven to 350 degrees F. Grease or line two baking sheets with parchment paper and set aside.
Beat the butter, sugars, and molasses with an electric mixer or by hand until light and fluffy (about 2-3 minutes). Add the vanilla; beat until combined. Beat in the eggs, one at a time. Add the flour, baking powder, baking soda, cinnamon, and salt. Stir in oats.
Drop the dough in 2-tablespoonful mounds 2-inches apart onto the prepared baking sheets. Bake for 12-15 minutes or until edges are lightly golden. Cool for 10 minutes before assembling.
Beat softened cream cheese, butter, powdered sugar, and vanilla until light and fluffy. Spread the filling on the flat side of half of the cookies. Sandwich them with the remaining cookies. Store in refrigerator for up to 4 days.