Heat the oven to 350°F (175°C) and grease an 8-inch square pan.
Place the dates and boiling water in a bowl. Stir in the baking soda and rest for 10 minutes, then mash lightly.
Whisk flour and baking powder in a bowl. Beat the butter and brown sugar until light, then beat in the eggs and vanilla. Fold in the dry ingredients and date mixture.
Bake:
Spread the batter in the prepared pan and bake for 35 to 40 minutes, until just set and a skewer comes out with moist crumbs.
Cool for 10 minutes while you make the sauce.
Make the Sauce and Serve:
Melt the butter in a saucepan. Add the brown sugar, cream, and salt; simmer for 3 to 4 minutes until glossy.
Poke the warm pudding all over with a skewer and pour over half the sauce. Cut into squares and serve with ice cream and the remaining sauce.
Notes
The sauce can be made two days ahead and rewarmed gently.
For a deeper flavor, replace a tablespoon of the cream with dark rum or brandy.