Preheat the oven to 350 degrees F (175 degrees C). Butter 2 baking sheets.

Bring dates and water to a simmer in a saucepan. Stir in baking soda and let simmer until most of the water is absorbed.

Beat brown sugar and butter together using an electric mixer until creamy. Add the date mixture, egg, and vanilla extract. Mix in flour, baking powder, and salt. Drop tablespoonfuls of dough 2 inches apart onto the prepared baking sheets.

Bake in the preheated oven until edges are golden, 13 to 15 minutes.

Meanwhile, stir heavy cream, butter, and brown sugar together in a sauce pot. Let boil for 3 minutes, stirring constantly. Stir in vanilla extract.

Let cookies cool before drizzling with warm toffee sauce.