I know of at least one custom at menarche for Jews which occurred (to my knowledge, it may be wider spread) in Yemen, which is the mother took the daughter and took some melted butter and pitot, put the daughters hands in a bowl, and poured melted butter over her hands and arms, while breaking off the chunks of pita into the bowl, while explaining that this is so that blessing will flow from her hands always, and charity will flow from her hands to the poor. I have to say I rather like this custom, and think if I had daughters, I’d definitely add it to my own.