Preheat the oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a large mixing bowl, cream the softened butter and granulated sugar until the mixture becomes light and fluffy. Beat in the egg and vanilla extract until fully incorporated.
In a separate bowl, whisk together the flour, cocoa powder, baking soda, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, mixing just until a smooth chocolate dough forms.
Scoop small portions of dough onto the prepared baking sheets, leaving enough space between each cookie. Gently flatten each dough ball slightly with the palm of your hand or the bottom of a glass.
Bake until the cookies are set around the edges and no longer look glossy in the center. Allow them to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.
While the cookies cool, prepare the filling by beating the butter until creamy. Gradually mix in the powdered sugar, vanilla, salt, and enough cream to create a smooth, fluffy buttercream.
While the cookies are still slightly warm, top each one with broken Oreo cookie pieces, a sprinkle of finely crushed Oreo cookie crumbs, and a few white chocolate chips, gently pressing the toppings into the cookies before letting them cool completely.
