If all you need to do is hear and capture Windows default output audio, then you don't need to do anything special-- just set the headphone as the default audio device, and tell OBS to capture it.
The issue comes if or when you want to be able to hear other audio-- say, monitor your own microphone, or hear media sources or capture cards connected to OBS.
OBS has an audio monitoring feature; it allows you to pick an audio output device to use for monitoring (Set it in Settings > Audio) and in the Mixer you can set which sources you want to monitor by setting them to "monitor and output" (meaning you hear them and they go in your stream/recordings).
The problem in the second scenario is that you can't use your windows default audio device as your monitor if you are also capturing it. This causes echo. In this scenario, you can either set default audio to a device you're not using (say, set it to your loudspeakers, but don't power them on) and then set the Monitor to be your headphones, and turn "monitor and output" for all the sources you want to hear, and just "output only" for stuff you need OBS to record or stream, but that you don't need to hear.
Depending on your needs it may also be useful to have software that gives you virtual audio devices and more options:
https://obsproject.com/forum/resour...nagement-for-1-and-2-pc-streaming-setups.397/
