Prepare the Ice Cream:
1.1 Warm the cream, milk, coffee, and vanilla seeds in a pan until steaming.
1.2 Whisk the sugar and egg yolks in a bowl or a free-standing mixer until pale. Then, pour the warmed cream and milk over the yolk mixture, whisking constantly.
1.3 Return the mixture to the pan and cook slowly over low heat, stirring constantly, until it coats the back of a spoon or reads 82°C on a digital thermometer. If it scrambles a bit, strain the mixture through a fine sieve.
1.4 Cool the mixture completely before adding the rum. Churn in an ice-cream maker until set, then freeze until needed.