Preheat the oven to 350°F. Grease a 9-inch square baking pan and line with parchment paper.
Soak the dates.
Place the chopped dates in a heatproof bowl. Pour the boiling water over the dates and stir in the baking soda. Let sit for 10 minutes. Do not drain.
Blend the dates.
Blend the softened dates together with all of their soaking liquid until mostly smooth.
Add the pumpkin, butter, and sugars.
Add the pumpkin purée, softened butter, dark brown sugar, and granulated sugar to the date mixture. Mix until thoroughly combined and the butter is evenly incorporated.
Add the eggs one at a time, mixing well after each addition. Mix in the vanilla.
Combine the dry ingredients.
In a separate bowl, whisk together the flour, baking powder, salt, cinnamon, ginger, and nutmeg.
Finish the batter.
Add the dry ingredients to the wet ingredients and gently mix just until no streaks of dry flour remain. Do not overmix.
Bake.
Spread the batter evenly into the prepared pan. Bake for 35–40 minutes, beginning to check around 32–33 minutes. The center should spring back lightly and a toothpick should come out with moist crumbs but no wet batter.
Make the toffee sauce.
While the cake bakes, combine the butter and dark brown sugar in a medium saucepan over medium heat. Cook, stirring, until the butter is melted and the mixture is combined.
Slowly pour in the heavy cream while stirring. Bring to a gentle simmer and cook for 4–5 minutes, stirring frequently, until smooth, glossy, and slightly thickened.
Remove from the heat and stir in the vanilla and salt. Taste and add another small pinch of salt if needed.
Soak the cake.
Allow the baked cake to cool for about 5 minutes. Use a skewer or toothpick to poke holes evenly over the surface.
Slowly pour ½ cup warm toffee sauce over the cake. Allow it to absorb for a minute or two. If you'd like the cake stickier, add up to another ¼ cup.
Reserve the remaining sauce for serving.
Rest.
Allow the cake to sit for 10–15 minutes so the sauce can soak into the crumb.
Serve.
Serve the cake warm with a scoop of vanilla bean ice cream, additional warm toffee sauce, and a pinch of flaky sea salt.
Notes
Dates: Don't drain the soaking water. It gets blended directly with the softened dates.Pumpkin: Make sure you're using pure pumpkin purée, not pumpkin pie filling.Toffee sauce: Start with about ½ cup over the cake. You can always add more, but saving plenty for serving gives you the best of both worlds.Serving: This is significantly better warm. If the cake has cooled completely, gently reheat individual servings before adding ice cream.Make-ahead: Both the cake and sauce can be prepared ahead. Refrigerate separately and gently reheat before serving.Mixing method: The butter and sugars are mixed directly into the pumpkin-date mixture rather than creamed separately. This gives us that incredibly moist, dense, sticky texture and also makes the recipe easier.