Preheat oven to 350°F. Line a standard muffin tin with cupcake liners and set aside.
In a small bowl, whisk the flour, baking powder, and salt together to combine. Set aside.
Using a hand mixer or a stand mixer fitted with the paddle attachment, cream the butter with the sugar until smooth. Add the prepared egg replacer and vanilla extract and mix to combine. Add the dry ingredients in thirds, alternating with the milk. Be sure to start and end with the dry ingredients, and beat briefly after each addition. Fold in the chopped cookies.
Spoon batter into the cupcake liners, filling a little over halfway full. Bake for 18-20 minutes, or until a toothpick inserted into the center of a cupcake comes out clean. Cool completely before frosting.
To make the Oreo buttercream frosting:
Using a hand mixer or a stand mixer fitted with the paddle attachment, beat the butter until smooth and creamy, about 3-4 minutes. Add the powdered sugar and cookie crumbs and continue to beat until fully incorporated. Add milk, one tablespoon at a time, until the buttercream reaches a piping consistency. Pipe or spread the frosting onto the cooled cupcakes
Be sure to follow the instructions on the package of Bob's Red Mill Egg Replacer. Once mixed with water, the egg replacer must sit for just a few minutes to thicken.
If you are not looking to replace eggs, you should be able to use 1 egg instead of the egg replacer.
My favorite chocolate sandwich cookies to use are gluten free Oreos or Glutino cookies.