1. Oil and flour an 8-inch square pan.
2. In a bowl, mix 1 cup all-purpose flour, granulated sugar, 1/4 cup chocolate chips, 2 tablespoons cocoa, baking powder, and salt. Add 2 tablespoons salad oil and 1/2 cup buttermilk; stir until the thick batter is evenly moistened. Scrape batter into prepared pan and spread level.
3. In the same bowl (no need to wash), mix brown sugar with remaining 1/4 cup cocoa and 1/4 cup chocolate chips. Scatter over batter in pan. Evenly pour remaining 1 cup buttermilk over brown sugar mixture; do not stir.
4. Bake in a 350° oven until edges of cake feel firm and spring back when lightly pressed, about 40 minutes.
5. Let cool in pan on a rack at least 15 minutes. Serve hot, warm, or at room temperature in bowls, scooping under cake to pan bottom to include pudding with each portion.