Preheat oven to 350°F (175°C) and grease two 12-count doughnut pans.
Prepare Oreo Doughnut Base: Whisk 2 cups flour, cocoa powder, 3/4 cup granulated sugar, 2 tsp baking powder, and 1/2 tsp salt. In a separate bowl, whisk 2 eggs, whole milk, 1/4 cup melted butter, and 1 tsp vanilla. Combine wet and dry, then fold in 1 cup crushed Oreos.
Prepare Chips Ahoy Doughnut Base: Whisk 2 cups flour, brown sugar, 1/2 cup granulated sugar, 2 tsp baking powder, 1/2 tsp baking soda, and 1/2 tsp salt. In a separate bowl, whisk 1 egg, buttermilk, 1/4 cup melted butter, and 1 tsp vanilla. Fold in mini chocolate chips and 1 cup crushed Chips Ahoy.
Pipe Oreo batter into one pan and Chips Ahoy batter into the second pan, filling each cavity 3/4 full.
Bake for 10-12 minutes or until a toothpick inserted comes out clean. Cool in pans for 5 minutes then transfer to wire racks.
Create Vanilla Glaze for Oreo doughnuts by whisking powdered sugar with 3 tbsp milk. Create Chocolate Ganache for Chips Ahoy doughnuts by melting 1/2 cup chocolate chips into 1/4 cup warm heavy cream.
Dip cooled Oreo doughnuts into vanilla glaze and top with remaining crushed Oreos.
Dip cooled Chips Ahoy doughnuts into chocolate ganache and top with remaining crushed Chips Ahoy.