Preheat oven to 180°C.
To make the batter, beat eggs with sugar until frothy.
Add vanilla, salt and rum, and beat.
Then whisk flour into the egg mixture, little by little, continually beating.
Add milk and whisk well.
Arrange figs, cut side up, in a lightly buttered gratin dish (or an ovenproof dish). Then pour the batter over the top, though a sieve. Dot with small dollops of butter and cook in the oven for about 40-45 mins until puffed and golden.
Sieve icing sugar over the top, before serving with ice cream or whipped cream.