First, I started watching different youtube videos on how to repair Bluetooth headsets. Basically, the kind of headset I like is the same across different brands and models. They are probably manufactured at the same Chinese factory, with very minor differences, and the same fundamental design. This was the most helpful video for me.
After I was ready to begin, I took apart my headset. While it was apart, I touched the soldering iron to the connections for the actual broken earbud. I removed it, stripped the plastic ear covers to use later, and then threw away the broken min-speaker.
Next, I cut a working headphone out from it's connection, stripped the leads, and then soldered that into the position that I removed from the previous step.
I then powered up (with everything disconnected) to make sure things worked. They worked, and I then reassembled everything, and it worked.
The number one "gotcha" is making sure you have enough slack in your new replacement headphone. Mine were too tight, and the lack of slack pulled the entire headset up, off my neck, when I was wearing it. That was pretty uncomfortable.
Notice how the new speaker wire is super short compared to the existing speaker wire - this is uncomfortable.
This was 100% not an efficient use of my time. It makes way more sense to throw away your broken pair, and buy a new one, unless you make minimum wage or less. It's like $9 (free shipping) from the link I shared above. However, I like repairing things. It's been a while since I did any electronics projects, and it was fun. Plus, I had a set of headphones where the speakers still worked, but the jack was sort of messed up. It was fun combining two broken things into one working thing.