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Preheat the oven to 325 degrees F.
Making the brownies: Line a baking dish with parchment paper and grease with the butter. Pour the brownie batter into the baking dish, then evenly scatter spoonfuls of the goat cheese mixture over the batter. With a knife, score the surface into a pattern.
Bake the brownies for 40 minutes. When done, remove to a wire rack to cool. Once cool, cut the brownies into bars, remove them from the baking pan and refrigerate.