Preheat your oven to 350°F. Line a 9x9-inch baking dish with parchment paper, leaving overhang on the sides for easy lifting.
Add the chopped dates and baking soda to a bowl. Pour the hot milk over the top, cover, and let sit for 10 minutes to soften. After 10 minutes, mash the dates with a fork until mostly broken down and thick.
In a large bowl, whisk together the melted butter and dark brown sugar until glossy and combined. Whisk in the vanilla extract, then add the eggs and mix until smooth.
Stir the mashed date mixture into the butter mixture until fully incorporated.
Add the all-purpose flour, baking powder, and salt. Gently fold until just combined.
Add the cocoa powder and espresso powder. Pour in the warm water and mix until smooth and no dry streaks remain. Do not overmix.
Pour the batter into the prepared 9x9 pan and smooth the top. Bake for 25 to 26 minutes, or until a toothpick, skewer, or fork inserted into the center comes out with moist crumbs.
While the cake bakes, make the chocolate toffee sauce. In a saucepan over medium heat, melt the butter. Add the brown sugar and whisk until dissolved and bubbling.
Stir in the heavy cream and simmer gently for 3 to 5 minutes until slightly thickened.
Remove from heat and stir in the chopped chocolate and vanilla extract. Mix until smooth and glossy.
Once the cake is done, let it cool slightly. Poke holes all over the warm cake using a toothpick, skewer, or fork.
Pour some of the warm chocolate toffee sauce over the cake, letting it soak in. Slice the cake into 9 pieces.
Serve each slice warm with a scoop of vanilla ice cream and more toffee sauce on top to enjoy.