Preheat the oven to 350 degrees F. Grease and flour a 12- to 15-cup bundt pan. Using an electric mixer, beat the oil, buttermilk, eggs, vinegar and vanilla on low until well combined.
In a separate bowl, sift the flour, sugar, baking soda, baking powder, salt and cocoa together. Slowly add them to the wet mixture until just combined. Scrape the bowl and mix again.
For the Brownie Batter:
Separate out 1 2/3 cups batter. Whisk 3 tablespoons cocoa powder and the melted chocolate into the batter. Set aside. Pour 2/3 of the remaining velvet batter into the bundt pan.
Add the brownie batter to the bundt pan and gently smooth over the top covering all areas. Do not swirl. Pour the remaining 1/3 velvet batter over the brownie batter.
Bake for 55-65 minutes until set in the middle. After 55 minutes check the center with a wooden skewer. If it comes out clean, the cake is done.
Allow the cake to cool for at least 20 minutes in the pan. Then carefully flip it out onto a cake plate. Allow it to cool completely before adding the glaze.
For the glaze:
Whisk 6 tablespoons of heavy cream with the powdered sugar and vanilla paste. If the mixture is too thick to pour add a little more cream, until it is thick and slow pouring.
Drizzle the glaze over the top of the cake with a spoons or whisk. allow the glaze to dry before covering.