1. Make the birthday cake ice cream and allow it to freeze for at least 6 hours before using it in the cookie recipe.
2. Make the cookies. Preheat the oven to 350 F. In the bowl of your stand mixer fitted with the paddle attachment, or using a handheld mixer, beat the butter and both sugars together until fluffy, about 2 minutes. Add the egg yolks and vanilla, and beat again for another minute, scraping down the sides as necessary.
3. In another mixing bowl, sift together the flour, cocoa powder, and salt. With the mixer running on low, add the dry ingredients to the wet, beating until just combined. Turn out the dough onto a lightly floured surface, and using your fingers, shape the dough into a log shape. Place the dough on a piece of parchment paper, and using a lightly floured rolling pin, roll it out into a rectangle, 3mm thick. Cut another piece of parchment paper to 7 1/2″ x 8″ and place it over top of the rectangle of dough. Trim the excess dough around the sides of the top parchment piece. Peel off the top piece of parchment paper, and using a measuring tape, cut the dough into either 4 or 6 even rectangles, but do not pull the dough apart! Using the scraps of dough you previously gathered, create another rectangle of dough the same shape and thickness (you should have no dough left) and cut into the same amount of rectangles. You’ll have either 8 or 12 in total! Prick all of the cookies with a fork a few times.
4. Place the rectangles of dough (keeping them on the parchment) on a baking sheet and bake for 10-11 minutes, or just beginning to set. Allow them to cool completely.
5. Prepare the ice cream. Place the ice cream in the fridge for an hour to thaw slightly. After an hour, line a rectangular container or a large baking sheet with parchment paper. Whatever you use, it needs to be at least the size of your cookies! Empty the thawed ice cream out onto the parchment paper, and use a spatula to smooth out the ice cream to 1″ thickness and top with another piece of parchment paper, smoothing it out completely and evenly. Freeze for 30 minutes – 1 hour.
6. Make the sandwiches. Remove the ice cream from the freezer. Remove the top layer of parchment paper, and lay the slab of ice cream on top of one half of the cookies. Cut through the ice cream on top of the cookies to match the shape of the cookies underneath. Pull the cookies apart, and top each with another cookie. Decorate the sides immedaitely with sprinkles, nuts, or mini chocolate chips. Wrap each cookie in parchment paper and freeze the sandwiches for 2-3 hours.

Ice cream sandwiches will keep in the freezer for at least two months. They will still be safe to eat after that, but the texture of the ice cream will begin to deteriorate.