Preheat your oven to 350°F (175°C).
Prepare caramel by melting sugar in a saucepan over medium heat until golden brown. Pour it into a mold, coating the bottom and sides.
In a bowl, whisk eggs, milks, vanilla, salt, and rum. Strain the mixture to remove any lumps.
Pour the mixture into the caramel-lined mold. Place the mold in a roasting pan filled with hot water halfway up the sides (creating a bain-marie).
Bake for 45–50 minutes or until a knife inserted in the center comes out clean.
Cool to room temperature, then refrigerate for at least 4 hours.
To serve, loosen the edges with a knife, invert onto a plate, and drizzle with remaining caramel.
