Preheat the oven to 350 degrees F. Grease and flour an 8x8-inch square pan.
MAKE THE CAKE BATTER:
In a medium bowl, combine the flour, sugar, chocolate chips, cocoa powder, baking powder and salt. Add the oil and buttermilk; stir until the thick batter is evenly moistened. Scrape the batter evenly into the prepared pan.
ADD THE TOPPING AND BAKE:
In the same bowl (no need to wash), combine the brown sugar with the cocoa powder and chocolate chips. Scatter the mixture over the batter in the pan. Evenly pour the remaining 1 cup buttermilk over the brown sugar mixture; do not stir.
Bake until edges of the cake feel firm and spring back when lightly pressed, about 40 minutes.
Let the cake cool in the pan on a rack for at least 15 minutes. Serve hot, warm, or at room temperature in bowls, scooping under the cake to the pan bottom to include pudding with each portion. It's great served with vanilla ice cream!