Preheat the oven to 200C/400F/Gas 6.
Cut the chocolate into small pieces and melt with the butter in a heatproof bowl over a pan of simmering water. As soon as the chocolate has melted, remove from the heat and add the vanilla extract, then stir in the warm water and sugar. Continue to mix until smooth. Lightly beat the egg yolks and whisk them into the chocolate mixture. Fold in the sifted rice flour and gluten-free baking powder, making sure there are no lumps.
Whisk the egg whites in a large, scrupulously clean bowl until stiff peaks form. Fold gently into the chocolate mixture and pour into the greased pie dish or ramekins.
Put the pie dish into a bain marie of hot water and bake for 10 minutes (for the single dish), then reduce the temperature to 160C/325F/Gas 3 for a further 20-30 minutes. If you are making individual dishes, they will be cooked in about 15 minutes at 200C/400F/Gas 6. The pudding should be firm on top but still soft and fudgy underneath. Dust with gluten-free icing sugar and serve hot, warm or cold with softly whipped cream.