Preheat the oven. Heat the oven to 180°C/350°F, or 160°C fan-forced.
Prepare the baking dish. Use one 5–6 cup ceramic or glass baking dish, approximately 1.25–1.5 litres, or six 200 ml ramekins. No greasing is necessary.
Melt the butter gently. Place the butter in a heatproof bowl and microwave in 20-second intervals until almost melted. Whisk until completely melted using the residual heat. The butter should look milky rather than like a pool of yellow oil.
Make the lemon batter. Whisk the sugar, lemon zest and vanilla into the melted butter. Add the lemon juice and egg yolks and whisk until combined. Add the flour and whisk until smooth, then gradually whisk in the milk. The batter will be quite thin.
Whip the egg whites. In a clean bowl, beat the egg whites with a handheld mixer or stand mixer until stiff peaks form.
Fold gently. Add a large scoop of the whipped egg whites to the batter and fold with a rubber spatula. Add the remaining egg whites and gently fold until incorporated. A few small lumps of egg white are perfectly fine.
Fill the dish. Pour the batter gently into the baking dish. If using ramekins, use a ladle and scoop from the bottom as well as the surface so each ramekin receives an even mixture of batter and fluffy egg white.
Prepare the water bath. Place the baking dish or ramekins inside a larger roasting pan. Carefully pour boiling water into the roasting pan until it reaches halfway up the sides of the baking dish.
Bake. Bake for approximately 35 minutes for one large dish or 30 minutes for ramekins. The top should be golden and lightly set, while the pudding will still jiggle slightly because of the lemon sauce underneath.
Rest and serve. Let the pudding rest for 5 minutes. Dust with icing sugar, then spoon out generous portions so everyone gets plenty of the warm lemon sauce. Serve with whipped cream or crème fraîche and optional lemon slices, raspberries and mint.