Mbed is an online compiler platform. There is nothing to install, just log in and start coding! One of the supported boards is the Nucleo-F401RE, which uses the exact same microcontroller as the FEZ. Use it as your target to build and compile to a .bin file, and then follow the instructions on the STM32 bootloader page to create a .dfu file and upload it to the FEZ.
This video shows how to use Mbed to program the FEZ (The FEZ and the BrainPad share the same processor).