Preheat oven to 350°. Stir together flour, next 3 ingredients, and 3/4 cup granulated sugar in a large bowl; stir in milk, oil, and vanilla. Spread batter in a lightly greased 8-inch square pan.
Combine brown sugar, cocoa, and remaining 1/2 cup granulated sugar in a small bowl; sprinkle over batter in pan. Using a spoon, gently drizzle 1 1/2 cups hot coffee over batter, being careful not to disturb layers. (Do not stir.)
Bake at 350° for 45 minutes or until a cake layer forms on top and layer springs back when touched. Let cool on a wire rack 25 minutes. Serve warm with whipped cream or ice cream.