Preheat the oven to 350°F and line 2 baking sheets with parchment paper.

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

In a large bowl, beat the softened butter, brown sugar, and granulated sugar until creamy and lighter in color, about 2 to 3 minutes.

Add the egg, egg yolk, and vanilla extract, then mix until smooth, scraping down the bowl as needed.

Add the dry ingredients to the wet ingredients and mix just until no dry streaks remain.

Fold in the white baking chips and chopped chocolate sandwich cookies until evenly distributed.

Scoop the dough into portions about 2 tablespoons each and place them on a plate or tray. Chill for 15 minutes.

Arrange the dough balls on the prepared baking sheets, leaving about 2 inches between them. Press a few extra cookie pieces onto the tops.

Bake for 11 to 12 minutes, until the edges are lightly golden and the centers still look slightly soft.

Let the cookies cool on the baking sheets for 5 minutes, then transfer to a wire rack to cool completely.