In a saucepan, combine about half the cream with the butter, corn syrup, and sugar.
Bring to a boil and cook over medium-low heat, stirring frequently, until the mixture is a deep amber (caramel) color. This could take 30+ minutes.
Carefully mix in the rest of the cream and the vanilla extract. The molten hot mixture will bubble vigorously.
Strain the caramel into a large Pyrex measuring cup or bowl and set aside.
Spray six ½-cup capacity ramekins with Baker's Joy or butter and flour. Set aside.
In a small saucepan, simmer the dates in the water until the water is nearly absorbed and the dates are soft, about 15 minutes. Put the dates and any liquid into your food processor and puree until very smooth.
Preheat the oven to 350°. Spray six ½-cup ramekins with Baker's Joy (a flour and oil nonstick baking spray).
In a small bowl, whisk together the flour, baking powder, baking soda, and salt.
With a mixer, beat the butter with the brown sugar until light and fluffy. Mix in the egg and vanilla, then the date puree. At low speed, mix in the dry ingredients.
Divide the batter between the ramekins. Smooth the tops if needed.
Bake for 20-30 minutes, or until a toothpick inserted into the centers comes out clean. Cool for about 5 minutes. Leave the oven on.
Unmold the cakes and invert them onto a cooling rack. Wipe the interiors of the ramekins to remove any crumbs. Spoon a tablespoon of caramel sauce into each ramekin.
Slice the cakes in half horizontally.
Return the bottom layers of the cakes to the ramekins, cut side up. Spoon another tablespoon of the caramel sauce into the ramekins and top with the remaining cake layers.
Spoon another tablespoon of the sauce over the cakes and spread evenly. Place the ramekins on a baking sheet and bake for 10 minutes.
Let the puddings cool for 5 minutes, then run an offset spatula or knife around the insides of the ramekins and invert each pudding onto a dessert plate.
Spoon some of the caramel around each cake if desired. May serve with a dollop of sweetened whipped cream or a small scoop of vanilla ice cream, if desired.
