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Grease or line an 8-inch pan with foil, then set aside.
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Preheat oven to 350 degrees.
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Stir butter and cocoa in large bowl until cocoa is completely dissolved.
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Add brown sugar and whisk to combine.
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Add one egg at a time, making sure each egg is fully mixed into the batter.
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Add balsamic vinegar, flour and salt, only stirring until no flour is visible, being careful not to over-mix.
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Pour batter into pan and set aside.
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Beat goat cheese, sugar, egg and vanilla until smooth.
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Dollop on top of brownie batter and carefully swirl with knife, but don't mix in completely.
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Sprinkle with chopped walnuts.
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Bake for approximately 25 minutes, or until a toothpick inserted in the middle comes out clean. Try not to over-bake.
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Cool, then cut into squares. Recipe makes 16 brownies.