Release the gimbal latch on your oven and preheat it to 350 degrees. Whisk together milk, white sugar, eggs and rum until the eggs are fully incorporated and it feels like the sugar has mostly dissolved.
Set 4-6 ramekins -- or just use ceramic coffee mugs -- in a baking pan and fill evenly with the milk mixture. Pour water into the pan to come about halfway up the filled portion of the cups. Seal the entire pan tightly with foil.
Bake for 50 minutes. Remove foil and insert a knife blade -- or marlinspike -- to test. If it comes out clean, they are done even if they still jiggle a bit. If not, seal the foil back up and give them another 5 minutes. When done, dump the water from the pan (or remove the cups) and chill them in the icebox for at least an hour or overnight.
When ready to serve, sprinkle the brown sugar as finely as possible over the top of each cup. If your oven has a broiler, broil for about 5 minutes -- watching carefully -- to melt the sugar without burning it. If you don't have a broiler (or propane torch, as my skipper has been known to use), simply letting the sugar sit for a few minutes should dissolve it ... not quite as glamorous as melting, but garnish with fresh fruit and no crew will complain!