Preheat oven to 350 degrees Fahrenheit. Line baking trays with parchment paper/silicone baking mats.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and sugars until light and fluffy. Add the eggs and vanilla. Mix until combined.
In a separate bowl, mix the flour, baking soda, cinnamon, and salt. Slowly add the flour mixture to the wet ingredients until almost combined. Add the oats and mix until incorporated. Scrape the bowl and mix again for 10 seconds. (To make sure no clumps of butter/sugar were hiding at the bottom of the bowl.)
Scoop 6 to 8 cookie dough balls onto prepared baking trays, about 2 Tablespoons each. Do not crowd the cookies. Bake for 11 to 12 minutes or until light brown. Let cookies rest on baking trays for a few minutes before removing them to a wire rack to cool completely.
CREAM FILLING: In a large bowl with an electric hand mixer, beat the butter until light and fluffy. Add powdered sugar and mix until completely incorporated. Add the vanilla and milk. Beat until light and fluffy, adding more milk 1 teaspoon at a time, if needed, until desired consistency.
To assemble, pipe or spread the cream filling on the bottom side of half the cookies. Place the remaining cookies on top, sandwiching them together. Store in an airtight container.