Preheat the oven to 350℉. Prepare a 9x13 baking pan with parchment paper and set aside.
In a large microwave-safe mixing bowl, add the butter, milk chocolate, and chocolate chips to the bowl and microwave in 30-second increments, whisking in between until the butter and chocolate are melted. Whisk until smooth.
Whisk the sugar into the chocolate mixture until the sugar dissolves. Next, add the 2 eggs and 2 egg yolks, whisking as you add them. Mix in the vanilla extract.
Use a wooden spoon or rubber spatula to mix in the sourdough discard, cocoa powder, and flour until there is no dry batter, making sure to scrape the sides of the bowl. Pour the brownie batter into the prepared baking dish. Bake for 35-40 minutes. You'll know the brownies are fully baked when you stick a wooden toothpick into the center of the brownies and moist crumbs stick to it. If there is still wet batter on it, they need to bake longer.
Allow the brownies to cool before cutting into squares and serving. Enjoy!