How to repair shifter housing
Seems like you have two options. I'm not sure this is your exact model but the broken piece should just unscrew.


Unscrew what's left and epoxy it together apart from the internal workings.
Buy a replacement cover. I couldn't find any online shops selling replacement covers, but a call to Shimano* will probably net you the exact piece you need. You'll need to know the model number which should be displayed somewhere and look like SL-xxxx. I can't imagine a new one will be more than $20.


*Shimano American Corp. (949) 951-5003