My Poppy had this happen, though I don't know if her injury was as severe as your chicken's. Poppy's was like if a person's fingernail was pried up from the nail bed, like an opened car hood (like you said). Her beak wasn't broken, though, just the top layer of it.
I didn't clip it because I was afraid to. It came off anyway the next day and her "raw" beak was icky and bloody. Poor girl... I offered her mash (feed mixed with water). She ate that for a couple of days and then went right back to eating her usual feed. She didn't peck at the ground as much, though. She is fine now, and the jagged edge where it broke off grew out rather quickly. Her beak is 100% normal now.