After you’ve made it to Undead Parish, you’ll unlock the elevators that take you back down to Firelink Shrine. From that elevator, you can roll and jump your way onto the roof over Petrus of Thorolund, where you’ll find the Undead Asylum F2 West key and the giant crow that will carry you back the the Northern Undead Asylum. It’s kind of hard to describe, so here’s a GIF:
Your second visit here is a lot harder, but will get you a few very useful items. The key from Firelink Shrine will get you access to the Rusted Iron Ring that lets you walk at normal speed through mud — which is invaluable for navigating Blighttown. You’ll also find the Peculiar Doll that will grant you access to the Painted World of Ariamis when you make your way to Anor Londo.
The optional boss in this area is a beefed up version of the Asylum Demon. Once you’ve picked up the items, there’s nothing else new here, so head back to Firelink and keep exploring.