Beat the eggs with the sugar.
Add the heated but not too hot milk, and the vanilla. Beat until the sugar melts.
Caramelize the rest of the sugar on low heat but don't let it burn.
Pour the caramel into bowls and pour on the egg-milk mixture. Arrange the bowls in a tray and pour in water, halfway up the bowls' walls.
Bake in a moderate 356°F (180 °C) oven but do not allow it to come to a boil.
Serve the creme caramels inverted and cooled onto a plate!