Just as files deleted from the hard drive of a PC can be recovered, so too can data that was saved on an external hard drive be recovered after such a drive is re-formatted. Data will be overwritten as new files are saved to the external hard drive. Formatting a drive only removes the address table or journal entry for files, it does not actually wipe them. Recoverit and EaseUS Data Recovery Wizard are popular tools used to recover data from re-formatted hard drives.
The free trial version of EaseUS will preview lost files that can be recovered, but you need to buy a license to actually begin recovering files. This does however let you know if there's something to recover. EaseUS allows you to target specific folders.
Not all recovery software will also rebuild the file directories on the external hard drive. Compressed files will be particularly difficult to recover.