Making Christmas Crack without brown sugar?
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Do you have molasses? Brown sugar is brown because it still has a bit of molasses in it. Otherwise there is no reason you can't make the recipe with white sugar, it will be different, but you might like it better. Take it as an opportunity to make your own Christmas Crack recipe - add a bit of something else to change it up like, I dunno, vanilla or whatever takes your fancy. Or make it with brown butter and caramel sugar as you said - why not? Then it will be your own creation.