-
Preheat the oven to 350°F. Butter an 8" square pan, or eight 8-ounce ramekins.
-
To make the pudding: Placed the cornstarch in a saucepan and add 2 tablespoons of the milk, stirring until no lumps remain. Add the remaining milk, sugar, split vanilla bean and its seeds (or vanilla bean paste), and salt. Heat, stirring occasionally, just until the mixture simmers, about 3 minutes. It will thicken slightly but no more than that.
-
Pour the mixture into the prepared pan, or divide it evenly among the ramekins (set them on a parchment-lined baking sheet first).
-
To make the cake: In a large bowl, whisk together the flour, sugar, baking powder, and salt. In another bowl, whisk together the egg, milk, butter, and vanilla. Add to the dry ingredients and mix just until moistened. Pour the batter into the prepared pan over the sauce. If using ramekins, divide the batter evenly among each.
-
Bake the cake(s) for 25 minutes (for either size), or until a toothpick inserted in the center of the cake comes out clean. The top of the cake will be golden brown, with some bubbles from the pudding around the edges. Remove from the oven, cool for 15 minutes, and serve warm.