With the rack in the middle position, preheat the oven to 400°F (200°C).
In a saucepan, bring the maple syrup and cream to a boil. Pour into a 10-cup (2.5 litre) soufflé dish.
In a bowl, combine the flour, baking powder, and salt.
In another bowl, cream the butter and sugar with an electric mixer. Add the eggs, one at a time, and beat until smooth. At low speed, add the dry ingredients alternately with the milk and vanilla. With an ice cream scoop or large spoon, spread the dough on the hot syrup. Place the dish on a baking sheet.
Bake for about 40 minutes or until a toothpick inserted in the centre of the cake comes out clean. Serve warm or cold.