Preheat the oven to 350°F (180°C or 165°C for a fan oven).
Place an oven rack in the middle of the oven.
Butter an 8 inch baking pan (or a 2.4 litre heart shaped Le Creuset baking dish).
Start with the cake, combining the flour, cocoa, baking powder, baking soda and salt in a medium bowl. Set aside.
Cream the butter and sugar in an electric mixer.
Add the egg and vanilla, beating until smooth.
Add the dry ingredients alternately with the milk.(Keep the mixer on low to do this.)
Blend until mixed.
Pour the batter into the prepared pan. Place the pan on a baking sheet and set aside.
Place the sugar, cocoa powder and cornstarch in a medium saucepan. Stir to mix.
Add the dark chocolate, single cream, water and blueberries.
Place the saucepan on the stove top over medium heat and bring the mixture to the boil, stirring constantly. (This may take a little while; don't rush the process or the mixture will scorch.)
Reduce the heat and simmer the mixture for 30 seconds just to bring it together.
Pour the hot sauce over the cake batter.
Place the baking sheet with the cake pan on top in the middle of the oven.
Bake for 45 to 50 minutes, watching the cake carefully after 40 minutes. The cake is done when a skewer inserted in the centre comes out clean-ish, bearing in mind there is a sauce underneath the cake. There shouldn't be any actual cake batter clinging to the skewer.
Remove the pudding cake from the oven and cool a bit in the pan. You can serve the cake warm or cold. Leftovers will keep in the fridge for about 2 days.