To make chocolate sauce, stir condensed milk in a small saucepan, over medium heat until hot.
Add chocolate. Whisk until smooth, then whisk in milk and rum. Remove from heat and cover to keep warm.
Bring milk, sugar, butter and vanilla beans and seeds to a boil in a medium saucepan.
Discard vanilla beans. Remove from heat.
Sift in flour. Stir with a wooden spoon until combined and dough comes away from side of pan. Remove from heat.
Stand, covered with plastic wrap, for 3 minutes.
Beat in egg yolks with wooden spoon, one at a time.
Spoon dough into a piping bag fitted with a 2cm star nozzle.
Heat oil to 180°C (when a cube of bread turns golden brown, oil is hot enough).
Pipe 5cm lengths into oil, cutting off the dough with a sharp knife.
Deep fry churros until golden brown, then drain on absorbent paper.
Dust with caster sugar and serve with chocolate sauce.