I recently had a root canal done through a crown and now I need the hole of the top surface filled. My dentist office says I need a "core build up" which is quite expensive. Don't I simply need a filling?

If there's a crown there, I would think so. But, your dentist should be the expert.

It would depend if there is decay under the crown. If there is, you'd need to have a core build up done to support a new crown.

If you need a new crown, yeah you need the core.. if he is charging you for a core to simply put amalgam or composite in the hole in the top of the crown (which does not even need freezing most times, that's not right... he should charge for a "one surface restoration"