Put the dates in a bowl and cover with the 1 cup boiling water to soften, at least 5 minutes. Heat the oven to 350 and grease a deep 9-by-13-inch baking dish.

Combine the 3 tablespoons butter, baking soda, a pinch of salt, Demerara sugar, 1/3 cup plus 1 teaspoon dark brown sugar, eggs, flour and vanilla extract in a food processor and pulse until just combined. Add the dates and 1/2 cup of the water to the mixture; pulse until nearly smooth (specks of dates should remain visible).

Pour the mixture into the baking dish and bake for about 30 minutes, until just firm to the touch. (When the pudding has finished baking, remove from the oven and heat the broiler. Put the rack about 4 inches from the heat source.)

Meanwhile, make the topping. Melt 5 tablespoons butter in a small saucepan over medium heat, then slowly add 1 cup cream and 6 tablespoons dark brown sugar and 1/8 teaspoon salt, whisking continuously until the mixture bubbles gently and comes together to form a smooth mixture; turn off heat.

In another small saucepan over medium heat, make the extra sauce. Melt 3 tablespoons butter, then slowly add 1 ¼ cups cream and 3 tablespoons dark brown sugar and 1/8 teaspoon salt. Repeat the process above.

Pour the topping (careful not to use the extra sauce) over the cooked pudding and place the whole thing in the broiler until it bubbles and looks sticky, 1 or 2 minutes (watch it closely). To serve, spoon into bowls and cover with the extra sauce. If you like, add a dollop of whipped cream.

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