This works for me on Windows 10.

You will need ffmpeg (free software) and HandbrakeCLI (open source (this also means "free")).

NOTE: You need to replace PATH\TO\ in :NOAUDIO and :HANDBRAKE with the path to those files in your system.

I put them all in one folder to make it easier, but you can put them wherever you like, as long as you put the proper paths in the code.

Save this as RecordDesktop.bat and run it to record your desktop:

@ECHO off
TITLE RecordDesktop

SET /P Input=Enter filename (.mp4 extension will be added automatically): 

SET /P =Press any key to begin the recording. Then, press Q to stop recording.< NUL
PAUSE > NUL
GOTO NOAUDIO

:NOAUDIO
PATH\TO\ffmpeg\bin\ffmpeg.exe -f gdigrab -framerate 30 -i desktop -vcodec libx264 %userprofile%\Videos\%Input%_TEMP.mp4
GOTO HANDBRAKE

:HANDBRAKE
PATH\TO\handbrakecli\HandBrakeCLI.exe -i %userprofile%\Videos\%Input%_TEMP.mp4 -o %userprofile%\Videos\%Input%.mp4
DEL %userprofile%\Videos\%Input%_TEMP.mp4

ECHO Finished!

SET /P =Press any key to exit.< NUL
PAUSE > NUL

explorer /select,%userprofile%\Videos\%Input%.mp4

EXIT