Spray a 1½-quart souffle dish with oil and set aside.

Combine the flour, baking powder, salt, ¾ cup of the granulated sugar, and ¼ cup of the cocoa in a mixing bowl. Add the milk, vanilla, and oil and mix into a stiff batter. Scrape into the prepared dish and smooth the top.

Mix the brown sugar, the remaining ¼ cup granulated sugar, and remaining ¼ cup cocoa in a small bowl; sprinkle in an even layer over the top of the batter. Pour the boiling water or coffee over all. Set the dish inside a 6-quart slow cooker and cover the top of the slow cooker with a folded kitchen towel, and then with the cooker lid. Cook on high for 2½ hours, or until the top of the cake is set and the bottom is still syrupy.

Cut into wedges or spoon onto plates, using the syrup on the bottom as a sauce.