Probably something you'll need to custom code, serial tends to be slow so you'd want a reasonable protocol that can pace and retry as needed. Perhaps something as simple as X-Modem, but something that can be restarted might be something to consider.
There's perhaps BSP code for the QSPI memory in question, or you could code it. I'd probably start by expanding that, and integrate the Erase and Write operation into the serial protocol chosen, and see how fast and robust you can make that.
