Preheat oven to 325°F and line a 9x9 inch baking pan with parchment paper, leaving an overhang on the sides to lift the completed goat cheese brownie out. In a bowl, sift together the flour, cocoa, and salt. Set aside.
Melt the butter and chocolate together and mix until combined. Add the granulated sugar and whisk until smooth. Allow the chocolate to cool to room temperature before continuing.
Add the eggs one at a time, whisking well after each addition until your batter is thick and shiny— about 2 minutes. Whisk in the goat cheese and vanilla, until there are no clumps or pieces.
Finally, whisk the flour mixture into the batter until everything is combined. Pour the batter into the prepared pan and bake for around 40-45 minutes or until a toothpick inserted into the center comes out clean. Remove from pan and allow to cool completely on a wire rack.