Heat oven to 350°. In a mixing bowl, stir together flour, sugar, 3 tablespoons cocoa, baking powder and salt. With a fork, mix in milk, oil and vanilla.
Spread the batter evenly in a lightly buttered 9-inch square baking pan.
Combine brown sugar and 1/4 cup cocoa; sprinkle over the batter. Slowly pour boiling hot water over the batter and brown sugar-cocoa mixture.
Bake chocolate pudding cake for 40 minutes. Let chocolate pudding cake stand for 5 minutes. Spoon into dessert dishes or cut into squares. Top chocolate pudding cake with ice cream or whipped topping. Enjoy!