Preparation Butter baking sheet. Cook sugar and water in heavy medium saucepan over low heat, stirring until sugar dissolves. Increase heat and boil without stirring until syrup turns dark amber color, swirling pan occasionally and washing down sugar crystals on side of pan and wet pastry brush, about 13 minutes. Mix in peanuts and butter, then sesame seeds. Immediately pour mixture onto prepared sheet. Cool completely. Break into pieces. Grind coarsely in processor using on/off turns. (Can be prepared 2 weeks ahead. Chill in airtight container.) Scoop ice cream into dishes. top with brittle. Spoon rum over; serve.
Preparation Butter baking sheet. Cook sugar and water in heavy medium saucepan over low heat, stirring until sugar dissolves. Increase heat and boil without stirring until syrup turns dark amber color, swirling pan occasionally and washing down sugar crystals on side of pan and wet pastry brush, about 13 minutes. Mix in peanuts and butter, then sesame seeds. Immediately pour mixture onto prepared sheet. Cool completely. Break into pieces. Grind coarsely in processor using on/off turns. (Can be prepared 2 weeks ahead. Chill in airtight container.) Scoop ice cream into dishes. top with brittle. Spoon rum over; serve.