With the rack in the middle position, preheat the oven to 180 °C (350 °F). Butter a 33 x 23-cm (13 x 9-inch) baking dish.
In a saucepan, combine the brown sugar, cocoa powder, and cornstarch. Add the water and cream and bring to a boil, stirring with a whisk. Stir in the vanilla. Set aside.
In a small saucepan, bring the milk and cocoa powder to a boil, stirring with a whisk. Let cool.
In a bowl, combine the flour, baking soda, and salt. Set aside.
In another bowl, combine the butter and sugar with an electric mixer until the mixture turns crumbly. Add the eggs, one at a time, and beat until smooth. At low speed, add the dry ingredients alternately with the cocoa mixture. Spoon the batter into the dish.
Carefully pour the hot sauce over the batter. Bake for about 45 minutes or until a toothpick inserted in the centre of the cake comes out clean. Serve warm or cool.