Heat oven to 325° . Place six 6-oz (5x1 inch) creme brulee dishes in large roasting pan.
In small saucepan, heat half and half carefully just until small bubbles form around edge. Remove from heat.
In bowl, combine eggs, 1/3 cup sugar, extract and rum. Slowly stir in half and half. Pour 1/2 cup custard into dishes. Place roasting pan on oven rack; pour hot water into pan so that it comes halfway up sides of dishes.
Bake at 325° for 15 min, until custard is just set. Transfer to wire rack, let cool 20 min. Refrigerate 2 hrs or overnight, covered.
Line large baking sheet with foil. In small saucepan, stir remaining 1/2 cup sugar and 3 tbsp water to dissolve sugar. Bring to boiling over high hear; boil without stirring, until amber in color (5-6 min). Pour onto prepared baking sheet, tilting to spread. Let cook until firm, 5 min. Gently tap to crack, pulse peices in food processor until finely ground. Makes 1/2 cup.
Stir 2 tsp carmelized sugar through medium sieve over each custard to cover evenly.