1. Whisk eggs until blended in a large bowl. Whisk in milk, cream, 1/2 cup sugar, vanilla seeds (or extract), salt, and rum.
2. Add bread and toss. Let soak for 45 minutes to 1 hour.
3. Meanwhile, set out a 9-inch round baking pan. Over medium/high heat, combine remaining sugar, vinegar and 1/2 cup water in a saucepan until dissolved. Cook without stirred 7-10 minutes until sugar is a dark amber. Remove from heat and add 1/4 cup water and swirl until smooth.
4. Working quickly, pour into the baking pan so it coats the bottom and some of the sides. Wait until firm, about 10 minutes.
5. Preheat the oven to 350 and set a kettle to boil. Butter uncoated interior of pan, spoon in the bread mixture, packing tightly to fit. Cover with a round of parchment paper.
6. Place the baking pan in a larger roasting pan. Pour enough boiling water into it to come halfway up the sides of the baking pan. Bake 75 minutes until a knife comes out barely clean.