Preheat oven to 350˚F. Lightly grease 2-3 doughnut pans.
In a large bowl, whisk together the flour, sugar, cornstarch, baking powder, baking soda, salt, and nutmeg.
In a small bowl, whisk together the buttermilk, eggs, butter, and vanilla extract. Mix into the flour mixture just until incorporated with no lumps. Gently fold in the crushed cookies.
Transfer the batter to a piping bag or a large ziploc bag with the corner snipped off. Pipe the batter into prepared doughnut pans. Each cavity should be about 2/3 full.
Bake in preheated oven until golden and the tops spring back when lightly pressed, 10-12 minutes. Allow to cool in the pan for 5 minutes, then transfer to wire rack to cool completely to room temperature.