Preheat the oven to 350 degrees. Lightly grease an 8"×8″ square nonstick baking pan. Make the chevre swirl by beating together the first four ingredients until smooth and well combined, then set aside.
Make the brownie base by whisking together the cocoa, sugar, salt, flour, and chocolate chips in a large mixing bowl. In a separate bowl, mix together the eggs, oil, and water until combined. Stir the wet ingredients into the dry ingredients and mix until just combined. Spoon half of the brownie batter into the prepared pan and smooth it out to create a bottom layer.
Next, create a second layer by alternating with large dollops of the chevre mixture and the remaining brownie base mixture, until all of the batter is in the pan.
Run the tip of a knife through the chevre and brownie batter to create a few distinct swirls on the top.
Bake the brownies for approximately 35-40 minutes. The brownies are done when a knife inserted into the middle of comes out with bits of moist crumbs. The brownies will continue to cook for a couple of minutes after they are removed from the oven. Place the pan on a cooling rack and allow to fully cool before serving.
For the Red Wine Pomegranate Sauce:
In a small sauce pot over medium heat, bring the wine and juice to a simmer, and reduce the volume by one-third. Stir in the sugar and allow it to dissolve completely. Mix together cornstarch and water to make a slurry, and whisk in to the wine reduction. Bring the sauce back to a simmer and cook for two minutes, just until the starch has been fully cooked out. Cool to room temperature and serve with the brownies.