Preheat the oven to 350°F. Grease and flour (see Baker’s Notes) the inside of a 10 to 12-cup capacity Bundt pan and set aside.
In a mixing bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In the bowl of an electric mixer fitted with the paddle attachment, mix the butter until smooth. Add the granulated sugar and mix on medium-high speed until light and fluffy, 2 to 4 minutes. Turn the mixer down to medium. Add the oil and mix until combined.
With the mixer on medium speed, add the eggs one at a time, allowing for each to fully incorporate before adding the next. Add the vanilla and mix to combined. Stop the mixer and scrape down the sides and bottom of the bowl.
Add about half of the flour mixture and mix on low speed until just incorporated. Stream in the buttermilk and mix until combined. Add in the remaining flour and mix until just incorporated. Do not over-mix. It is okay if there are still a few streaks of flour remaining.
Remove about two cups of the batter and place it in a separate bowl. Stir in the brown sugar, cinnamon, and cocoa powder until combined.
Using a mechanical cookie or ice cream scoop, dollop about a third of the plain buttermilk batter into the bottom of the pan. Add a layer of cinnamon batter on top and repeat. Gently swirl the batters together with the tip of a butter knife.
Bake the cake for 50 to 60 minutes, or until a wooden skewer or cake tester inserted into the center of the cake comes out clean.
Cool the cake for 20 minutes then unmold it from the pan. Do not let the cake completely cool in the pan (see Steps).