Grease a 13x9-inch baking dish. In a medium saucepan, combine sugar, brown sugar, butter and evaporated milk. Over medium heat, bring mixture to boiling while stirring constantly. Once boiling, boil constantly for 7 minutes without stirring.
Remove from heat and stir in marshmallow creme until blended in and melted. Let cool 15 minutes. Mix in peanut butter and vanilla, stir until smooth.