Preheat the oven to 350 degrees.

Prepare several large-rimmed baking sheets with parchment paper. Set aside.

In a medium bowl, whisk together the flour, baking soda, and salt. Set aside.

In a mixing bowl, beat the butter, peanut butter, sugar, and brown sugar together until fluffy, about 6 minutes.

Add the eggs, mixing until incorporated and creamy. Scrape down the sides as needed.

Add the flour mixture to the batter and beat just until blended.

Fold in the oats.

Using a medium cookie scoop, portion the batter onto the prepared baking sheets making sure the dough is about 2 inches apart.

Bake the cookies for 15 to 17 minutes or until set on the sides and slightly crinkled across the top.

Let the cookies cool completely on the baking sheets.

Once the cookies are cool, make the filling.

Start by beating the butter and peanut butter together until creamy.

Add the sugar a little at a time, scraping down the sides as needed.

Add just enough milk to reach your desired consistency.

Transfer the filling into a piping bag with the end snipped.

Pipe the filling onto a cookie. (As an alternative, a small scoop can also be used for the filling.) Then, place another cookie on top, twisting slightly to spread the filling to the edge.

Refrigerate the cookies until the filling is set.

Store in an airtight container in the refrigerator.