New Streaming PC Specs?

So basically I have been streaming using a stream PC to save some performance on my main rig and also the added benefit of the stream not going down when I dual boot.

I was trying to use a single board computer I had already but it can’t seem to do 1080p encoding without it being overloaded and the stream goes down.

So I was looking at upgrading this machine. I assume I don’t need anything too expensive because its soul purpose is to just run OBS. Wondering if any of you might know what CPU’s out there can do 1080P 60FPS streaming? I also considered going to a surplus store and grabbing an old machine but I am not sure what I should be looking for?