If you bought it as a gift and she broke it its her issue - why does it bother you if you gave it away. she has nothing to apologise for except maybe being a bit clumsy.
She doesn't have anything to apologise for. You gave her the spoon, so it was her spoon. It wasn't your spoon. Why does she have to apologise for breaking her own spoon? That doesn't make sense.
The only exception would be if she broke it just to spite you. If that happened, then she should apologise. How you would make that happen with the kind of person that would do that, I have no idea. My guess is, if you have someone so uncouth that they will break their gift to spite the giver, your not dealing with a person you should expect much back from anyway. You may just have to adjust your expectations. Either that or stop being friends with her. Seems rather drastic over a spoon, even one that cost you two tenners.