Cut the panettone into not too thick slices. Arrange 1 layer in a suitable tray or form and spray with rum.
For the custard, heat the milk with the sugar and vanilla. Beat the eggs very well and add them to the warm milk, stirring constantly with a mixer. Pour half of the cream over the panettone in the form.
On top, arrange another layer of panettone, sprinkle again with rum and add on the remaining cream.
Put the panettone cake with custard in a container in a water bath and bake in the oven at 392°F (200 °C) for 20-25 minutes.