Place the pitted dates in a bowl, cover with just-boiled water, and let them soak for 10–15 minutes until soft and plump, then drain well and blend into a smooth paste.
Preheat the oven to 175 °C (165 °C fan). Line a 20×30 cm brownie tin with baking parchment.
Mash bananas until smooth, then whisk together with the date paste, eggs, oil, and vanilla until combined.
In another bowl, mix flour, cocoa, baking powder, baking soda, and salt.
Fold the dry mix into the wet mixture until just combined (do not overmix)
Pour the batter into the prepared tin, spread evenly, and bake for 30–35 minutes, until a skewer inserted in the centre comes out with a few moist crumbs (not wet batter).
Allow the brownie to cool completely in the tin, then lift it out and cut into 16 squares.