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Preheat the oven to 350 degrees. Line an 8-inch square baking dish with foil. Spray the foil with cooking spray and set pan aside.
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Combine the butter and unsweetened chocolate in a microwave-safe bowl and heat in 30-second intervals, stirring after each interval, until melted and smooth. (Or you can do this in the top of a double boiler set over barely simmering water.) Set the mixture aside to cool for 5 minutes.
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Combine the sugar, eggs, and vanilla, in a large mixing bowl. Stir vigorously with a rubber spatula until well combined. Stir in the chocolate mixture.
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Add the flour, cake mix, and salt and mix until just combined.
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Pour half of the brownie batter into the prepared pan. Use an offset spatula to spread the filling into an even layer over the brownie batter.
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Dollop the remaining brownie batter over the filling, then carefully spread it out. Use a butter knife to swirl the batter and the filling together (don’t over-swirl).
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Bake 45 to 50 minutes, until the brownies have just begun to pull away from the pan at the edges and the center is still a little jiggly.
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Cool completely, then slice and serve. (The brownies are easier to slice neatly if you chill the overnight first.)
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Uneaten brownies can be stored in the fridge, tightly wrapped, for up to 3 days or in the freezer for up to 3 months.