so I am inserting some html in a block in the header and wanted to know how to including something like {$smarty.session.cart.amount} in the block. It wont process the request and I dont want to have to make a hook for it, I know I am missing something to have this happen, anyone that can help would be greatly appreciated.
You can't make a hook in an html block nor use template variables. It is an HTML block.
You can always create a custom block where you can use template variables (with a settings/schema that will provide the data). It is not a straight forward process and it is different between V2 and V3.