Prep: Preheat the oven to 350°F. Line a 13x18-inch baking pan (half sheet pan) with parchment paper.
Make the cookies: Whisk the wet ingredients together.
113 grams unsalted butter, 57 grams sourdough discard, 42 grams heavy whipping cream, 170 grams light brown sugar, 1 teaspoon vanilla extract
Fold the dry ingredients in. Stir the chocolate in until evenly distributed.
191 grams all purpose flour, ½ teaspoon baking soda, ½ teaspoon fine sea salt, 142 grams dark chocolate
Transfer the batter to the prepared baking sheet and using your hands press it thin so fills the entire sheet.
I like to add my cookie dough in dollops and press it in to the corners to make sure my entire baking sheet is covered. Don't be afraid to pinch off thicker sections to fill in any holes. Finely chopping your dark chocolate will make spreading the cookie dough out much easier.
Bake the cookie: Bake for 10 to 12 minutes or until the cookies look golden brown and set. Allow to cool completely in the baking pan.
Freeze the cookie sheet for about 15 minutes, this will allow it to set completely and prevent it from breaking when you assemble your ice cream sandwich.
Create a parchment sling: Line a 9x13-inch baking pan with parchment paper, making sure it folds over the edges. This will make it easier to handle your ice cream sandwich.
Make the ice cream: In the bowl of a stand mixer fitted with the whisk attachment (or using a hand mixer), add the heavy whipping cream and ground vanilla bean. Whisk, starting on low to avoid splattering, and gradually increase the speed as the mixture starts to thicken until you’re at full speed. Whisk until stiff peaks form.
452 grams heavy whipping cream
Add the sweetened condensed milk into the heavy cream mixture and fold to combine completely.
396 grams sweetened condensed milk, ¼ teaspoon vanilla extract
Assemble: Remove the cookie slab from the baking sheet and cut in half so you have two pieces that are about 9x13-inches. Place one of the pieces bottom side up into the prepared 9x13-inch baking pan.
Pour the ice cream into the baking pan on top of the cookie. Drizzle chocolate ganache (if using) into the ice cream and the swirl it around with a butter knife. Top with the second cookie piece, top side up.
Chill: Place the pan in the freezer and allow it to set overnight.
Store the cookies: Remove the pan from the freezer and lift up the giant bar to remove. You can trim off the edges for a clean look if you want, but totally optional! Cut into 12 bars. I cut in half long ways, then cut into 6 pieces on each side for ice cream bar shapes. You can also cut them square like brownies (4x3).
Serve immediately or wrap each individual one in plastic wrap and store in the freezer.