Heat oven to 350 degrees. You'll need a shallow baking dish.
Microwave butter and chocolate in a small bowl just until melted; stir with a whisk to combine, then stir in yolk until well blended.
Whisk flour, 3/4 cup granulated sugar, 1/3 cup cocoa, the baking powder and salt in a medium bowl until blended. Stir in 1/2 cup milk, the butter mixture and vanilla until smooth. Spread batter into an ungreased baking dish.
Mix remaining 1/2 cup granulated sugar, remaining 1/3 cup cocoa and the brown sugar in a small bowl with fingers or a fork until blended. Sprinkle over batter.
Heat remaining 2 cups milk in microwave just until simmering. Slowly pour over mixture in baking dish--Don't Stir.
BAke 45 minutes. Spoon into dessert bowls. Top each serving with a small scoop of ce cream. Serve immediately or pudding layer will be absorbed by cake layer.