Sending large ammount of data with USB
If you clock the STM32 with a 64MHz clock and use the over-sample by 8 mode then you can get up to 8Mbps data rates just using the UART.
The FTDI cables support data rates much faster than 115200 bps.  In some cases you may have to use the D2XX drivers instead of the COM port drivers.
TTL-232RG-VREG3V3-WE
3.3V TTL UART, up to 3Mbps baud rate.
https://www.ftdichip.com/Products/Cables/USBTTLSerial.htm
NOTE:  Due to 128 byte RX buffer and 1kHz USB full-speed frame timing.  Sustained transfer rate is limited to 1kHz * 128 bytes * 8 bits/Byte = 1.024,Mbps.
C232HD-DDHSP-0
3.3V TTL UART, up to 12Mbps baud rate.
https://www.ftdichip.com/Products/Cables/USBMPSSE.htm
NOTE:  Due to 1K byte RX buffer and 8kHz USB hi-speed frame timing.  Sustained transfer rate is limited to 8kHz * 1K bytes * 8 bits/Byte = 8.192 Mbps.
C232HM-DDHSL-0
3.3V TTL UART, up to 30Mbps
https://www.ftdichip.com/Products/Cables/USBMPSSE.htm
NOTE:  Due to 1K byte RX buffer and 8kHz USB hi-speed frame timing.  Sustained transfer rate is limited to 8kHz * 1K bytes * 8 bits/Byte = 8.192 Mbps.