In a medium bowl, mix together the all-purpose flour and cocoa powder; set aside.
In a large bowl, cream together the butter and brown sugar for about 1-2 minutes, until light and fluffy. Add the eggs, vanilla extract, baking soda and salt; mix until thoroughly combined. Fold in the oats until completely combined. Next, fold in the flour and cocoa powder mixture and mix until there are no longer any specks of flour.
Using a 2-inch cookie scooper, drop rounds of cookie dough onto a parchment-lined baking sheet, spacing the cookies about 2-inches apart and flattening each cookie slightly. Transfer the baking sheet to the oven and bake for 10-12 minutes, until the cookies’ edges are firm but the edges are still soft to the touch. Using a spatula, carefully transfer the cookies to a cooling rack.
While the cookies are cooling, make the peanut butter frosting. Add the room temperature butter, powdered sugar, whole milk and salt to a medium bowl. Using a standup mixer or a good ol' fashion spatula, beat all of the ingredients together until light, fluffy and smooth.
To assemble the sandwiches, scoop a teaspoon or two of peanut butter frosting onto the center of half of the cookies; smooth it out with a knife and place the remaining cookies on top, gently pressing on them to squeeze the filling so it reaches the edges.
Note: I used creamy natural peanut butter with no sugar added; if your peanut butter has sugar, I'd recommend scaling back on the powdered sugar and doing it to taste.