Preheat oven to 350F. Grease and line a 8x8" baking pan with parchment paper. Set aside.
Add the chocolate and butter to a small saucepan and melt over medium heat until smooth, whisk in the vegetable oil and set aside. In a medium sized bowl, whisk together the granulated sugar, brown sugar, and eggs until completely smooth. Add in the melted chocolate mixture and whisk until fully combined.
Sift in the cocoa powder, flour, baking soda, and salt and whisk until just combined. Be careful not to overmix.
Reserve half a cup and pour the rest of the batter into your prepared pan.
In a separate bowl, beat together the goat cheese, sugar, flour, and egg until smooth. Pour on top of the brownie base. Add small dollops of the remaining brownie batter atop the goat cheese layer, then with a knife carefully swirl it around.
Bake for about 30-35 minutes or until the brownies are set and a cake tester inserted into the center has moist crumbs attached. Do not overbake. Remove from oven and allow to cool.
Enjoy plain or with vanilla ice cream and some hot fudge!