Preheat the oven to 350°F. Line baking sheets with parchment paper and set aside.
Make the cookie dough.
In the bowl of a stand mixer (or in a large bowl using an electric hand mixer), beat butter, brown sugar, and sugar until creamy.
Add egg and vanilla and beat until combined.
Add flour, baking soda, cinnamon, and salt and mix until combined.
Add oats and mix just until blended.
Scoop tablespoons of dough and gently roll each into a ball.
Bake the cookies.
Place cookie dough balls on a cookie sheet and bake 10 minutes or until cookies are golden brown. Let cookies cool on the tray for a couple of minutes, and then transfer to a wire rack to cool completely.
Make the buttercream filling.
In the bowl of a stand mixer using the paddle attachment (or in a large bowl using a handheld electric mixer), beat butter on medium-high speed until smooth.
Add vanilla and salt and beat on medium-high speed until blended.
Add sugar slowly – one cup at a time – beating well on medium speed and scraping the bowl often. When all sugar is added the frosting will be slightly dry.
Add milk and beat on high speed until the frosting is light and fluffy.
Add the berry jam and beat until well blended.
Assemble the sandwich cookies.
Once the cookies are completely cool, spread half of the cookies with a thick layer of buttercream and top with the remaining cookies.
Notes
Storage: Store leftover cookies in an airtight container at room temperature for up to 3 days.