Two days before you plan to serve the dessert, combine the milk and vanilla bean in a saucepan and bring to a boil. Immediately turn off the heat and let cool to room temperature. Cover and refrigerate overnight to infuse the vanilla flavor into the milk. The next day, melt the butter. Whisk the eggs into the chilled milk mixture, then whisk in the rum and butter. Add the sugar and flour and whisk to combine. Refrigerate overnight.
Heat the oven to 400 degrees F. Thickly butter your baking molds (above) and chill until the butter is firm. Whisk the batter 1 more time to mix it thoroughly and pour or ladle into the molds, filling them not quite full. Bake until very, very dark brown on the outside, about 1 hour. Check them after 45 minutes to make sure they're dark brown but not turning black. When finished, they will be very dark, caramelized and chewy on the outside, tender and eggy on the inside. While still warm, turn out of the molds.