Put the sweetened condensed milk in a bowl (add 50 g more sugar to taste, but it is not absolutely necessary), add the same amount of milk (use the can to measure), the 6 eggs, the vanilla extract and the rum.
Mix well with the mixer.
Melt the sugar in an ovenproof dish on the stove until a caramel has formed, leave to cool for 10 minutes. Pour the egg-milk mixture over it.
Cook in the oven either in a water bath or directly (like a cake) until the mixture is firm (chopstick test).
Let cool in the tin, then turn out onto a plate.
In the oven (without a water bath):
20 min, covered with aluminum foil, to 220 ° C
20 min, covered with aluminum foil, to 200 ° C
20 minutes, without aluminum foil, at 180 ° C to get some color.
Best served with Dulce de leche (see recipe there).