1. Let 1 gallon of ice cream (1.5 quarts) sit at room temperature until soft, about 30 minutes. You want the ice cream to be soft not melted, otherwise the ice cream will refreeze with a gritty texture.
2. Prepare a 13×9-inch rimmed baking sheet with a piece of parchment paper. Spread softened vanilla ice cream into the pan and spread into an even layer. Place another piece of parchment paper on top and freeze until solid.
3. In a large bowl, whisk together 1 cup flour (140g), 1/2 cup unsweetened cocoa powder (50g), 1 tsp baking soda (4g), and 1/2 tsp salt (4g).
4. In the bowl of a stand mixer fitted with the paddle attachment, cream 3/4 c butter (156g) and 1 c sugar (220g) on medium speed until light and fluffy, about 2-3 minutes. Stop to scrape the sides of the bowl as needed.
5. Add 2 eggs, one at a time, mixing until thoroughly incorporated. Beat in 2 tsp vanilla extract (8g) and 1/2 c sourdough discard (140g) until combined.
6. Add the flour mixture and beat on low speed until just combined. Often times, I will finish mixing in the dry ingredients with a rubber spatula.
7. Spread the batter onto a buttered 18×13-inch rimmed baking sheet lined with parchment paper with an offset spatula. Try your best to spread into an even layer.
8. Preheat oven to 350 degrees F and bake for 12 to 14 minutes, or until the top of the sourdough cookie looks dry and the edges are starting to pull away from the baking sheet.
9. Allow the cookie layer to cool slightly in the pan, then run a small knife around the edges of the cookie. Carefully transfer the cookie with the parchment paper to a wire rack to cool completely.
11. Move the sourdough cookie onto a cutting board and remove the parchment paper. Cut the sourdough cookie in half, creating two 9×13-inch slabs.
12. Now, sandwich the frozen ice cream between the cookie slabs. Carefully wrap the Sourdough Ice Cream Sandwich completely in plastic wrap and freeze until firm, for at least 4 hours, but overnight is best!
13. When ready to serve, slice into 12-16 sandwiches with a warm serrated knife for clean slices.