Preheat your oven to 350°F (175°C). Grease a 9-inch round cake pan or a similar-sized baking dish.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In a large mixing bowl, cream together the softened butter and brown sugar until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
In a separate bowl, combine the chopped dates and boiling water. Let sit for about 10 minutes until the dates soften, then mash slightly with a fork.
Fold the date mixture into the butter and sugar mixture. Gradually add the dry ingredients, mixing until just combined.
Pour the batter into the prepared cake pan and smooth the top. Bake for 30-35 minutes, or until a toothpick inserted in the center comes out clean.
While the pudding is baking, prepare the toffee sauce by combining the heavy cream, dark brown sugar, butter, and vanilla extract in a saucepan over medium heat. Stir until the sugar dissolves and the mixture is smooth, then bring to a gentle simmer and cook for about 5 minutes.
Once the pudding is done, remove it from the oven and let it cool for 10 minutes. Carefully invert it onto a serving plate and drizzle half of the warm toffee sauce over the top.
Serve warm with the remaining toffee sauce on the side.