Preheat the oven to 350F and grease an 8x8 inch baking dish. Combine the chopped dates, boiling water, and baking soda in a bowl and soak for 10 minutes, then mash into a chunky puree.
Whisk the flour, baking powder, and salt in a medium bowl.
Beat the softened butter and brown sugar for 2 minutes, then beat in the yogurt and vanilla.
Stir in the date mixture with all its soaking liquid, then fold in the dry ingredients just until combined.
Spread the batter into the dish and bake for 30-35 minutes, until the center springs back when lightly pressed.
While the cake bakes, make the sauce: simmer the butter, brown sugar, heavy cream, and salt for 4-5 minutes until glossy and slightly thickened, then stir in the vanilla.
Poke the warm cake all over with a skewer and pour half the toffee sauce over it. Let it soak in for 10 minutes.
Cut into squares and serve warm with the remaining toffee sauce spooned over the top - a scoop of vanilla ice cream makes it perfect.
