Preheat< oven to 350 degrees F. Butter two 8 inch cake pans.
In the bowl of a stand mixer, add the flours, sugar, baking powder and salt, and mix together on low speed for 1 minute. With the mixer on low, add the butter, continuing until all the butter has been added.
Keeping the mixer on low speed, add the eggs one at a time, scraping down the sides of the bowl between additions. Slowly pour in the milk and vanilla and mix until combined. Increase the mixer speed to medium and beat for 2 minutes, until batter is smooth, scraping the sides of bowl as needed. Using a rubber spatula, gently stir in the sprinkles.
Bake for 30 - 35 minutes or until the cake is firm and slightly brown on edges.
Line 2 (8 inch) round pans with plastic wrap. Spread a pint of ice cream in each. Cover and refrigerate several hours or overnight until firm.
Place one cake round on a plate. Remove plastic wrap from one cake pan and top cake with an ice cream round. Layer another cake, ice cream, cake. Press lightly to make sure it's sticking together, then use a knife to trim any ice cream that might be hanging out over the cake. You want the sides to be pretty level.
Place cake in the freezer while you prepare frosting.
In the bowl of your mixer, beat butter and vanilla on medium speed until smooth. Slowly add powdered sugar, a little at a time, until just combined. Add heavy cream and beat on high for about 1 minute, until fluffy and smooth. Fold in sprinkles.
Frost the prepared cake. If ice cream begins to get melty, place cake back in the freezer until firm, then finish frosting. Once complete, garnish with the cookies if desired. Sprinkle the top with extra sprinkles for decoration.
Keep frosted cake stored in the freezer. Remove cake from freezer 10 -15 minutes prior to cutting and serving.