Sprinkle heatproof ramekins with 1/2 tbsp sugar each, moisten with a few drops of water. Caramelize the sugar in the ramekins on the hot stove top over medium heat until honey brown, then cool.
Then lightly brush the inside walls of the ramekins with oil.
Preheat the oven to 175 °C (convection oven 150). Stir the eggs with the remaining sugar until the sugar is dissolved. Mix in the espresso and rum and divide evenly among the ramekins.
Fill a suitable pan three inches high with hot water, place the ramekins in it and cook in the hot oven for twenty-five to thirty-five minutes, until the surface of the flans is elastically firm when poked with the back of a spoon.
Remove the ramekins from the water bath and cool.
To serve, loosen the edge of the flans with the tip of a knife, turn the flans out onto plates.