Preheat the oven to 350°F (175°C). Thoroughly grease a 10- to 12-cup Bundt pan, making sure to coat every groove.
In a medium bowl, whisk together the flour, cocoa powder, baking powder, baking soda, and salt.
In a large mixing bowl, beat the softened butter, granulated sugar, and brown sugar for about 3–4 minutes, until lighter and fluffy.
Add the eggs one at a time, beating well after each addition and scraping down the bowl as needed. Mix in the vanilla.
Combine the red wine and buttermilk in a measuring cup.
Add the dry ingredients to the butter mixture in three additions, alternating with the wine mixture in two additions. Begin and end with the dry ingredients and mix only until combined.
Spoon the batter evenly into the prepared Bundt pan and smooth the top.
Bake for 45–55 minutes, or until a toothpick inserted into the thickest part of the cake comes out with a few moist crumbs rather than wet batter.
Let the cake cool in the pan for 15 minutes, then carefully invert it onto a wire rack and cool completely.