Preheat the oven to 350°F. Line a 13x18-inch baking pan (half sheet pan) with parchment paper.
To make the cookies: In a mixing bowl, add the butter, sourdough discard, and heavy whipping cream and mix together until combined. Add the brown sugar and vanilla extract and mix to combine.
Next, add the dry ingredients: flour, baking soda, and sea salt and fold together until a cookie dough forms. Add the chocolate and fold together completely.
Transfer the batter to the prepared baking sheet and using your hands press it thin so fills the entire sheet. Alternatively, you can also place the dough between two pieces of parchment paper and roll it out as well.
Bake for 10 to 12 minutes or until the cookies look golden brown and set. Allow to cool completely in the baking pan.
Line a 9x13-inch baking pan with parchment paper, making sure it folds over the edges. Freeze the cookie sheet for about 15 minutes, this will prevent it from breaking as it’s so thin.
To 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.
Add the sweetened condensed milk into the heavy cream mixture and fold to combine completely.
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. Place the pan in the freezer and allow it to set overnight.
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.