Preheat oven to 375°. Line baking sheets with parchment paper or silicone liners.
Whisk together flour, baking soda, salt, and cinnamon. Stir in oats. Set aside.
Using an electric mixer, beat butter, brown sugar, and sugar until creamy. Add egg and vanilla, and mix well. Gradually add flour mixture, stirring until well blended.
Drop dough by rounded tablespoonfuls, 2 inches apart, onto prepared baking sheets. Bake 10-12 minutes. Cool on pan for 2-3 minutes, then remove to wire racks to cool completely.
Combine all ingredients in a medium bowl. Using an electric mixer on low speed, beat until combined. Then, increase mixer speed to high, and beat until light and fluffy.
Spread about 1 tablespoon of filling over the bottom side of half of the cookies. Top with remaining cookies so that the bottoms of the cookies are facing the filling.
Makes about 18 cream pies (36 cookies).