After some research, it appears ethtool
can be used to read and write to the eeprom (http://manpages.ubuntu.com/manpages/hardy/en/man8/ethtool.8.html):
ethtool -d|--register-dump ethX [raw on|off] [hex on|off] [file name]
ethtool -e|--eeprom-dump ethX [raw on|off] [offset N] [length N]
ethtool -E|--change-eeprom ethX [magic N] [offset N] [value N]
To dump eeprom, you can do ethtool -e ethX raw <on|off> offset <N> length <N>
.