In a small bowl combine half of dates, water, and baking soda and soak for 5 minutes. Drain dates, reserving liquid, and transfer to a medium bowl. In a separate bowl whisk together the flour, baking powder, and salt.

In the bowl of a food processor, combine remaining dates and brown sugar and pulse until blended, about five 1-second pulses. Add drained dates, reserved soaking liquid, eggs, and vanilla and process until smooth, about 5 seconds. With the food processor running, pour the melted butter through feed tube. Transfer the mixture to a medium bowl.

Gently stir dry ingredients into wet mixture just until combined. Distribute batter evenly among prepared  ramekins. Fill the roasting pan with enough boiling water to come halfway up the sides of the ramekins, making sure not to slash water into the ramekins. Cover pan tightly with aluminum foil, crimpimg edges to seal. Bake pudding cakes until puffed and small holes appear on the surface, about 40 minutes. Immediately remove ramekins from the roasting pan and cool on a wire rack for 10 minutes.

Continue to cook, stirring occasionally, until mixture looks bubbly and puffy, 3 to 4 minutes. Slowly pour in cream and rum, whisk just to combine. Reduce the heat and simmer until frothy, about 3 minutes. Remove from the heat, cover and keep warm. Set aside.