Here we go- it was actually way easier than I thought!
Step 1: remove back cover of mirror assembly. I marked the area with a red dot where you should start. Pull back and up with a slight pressure and the cover will pop right off. The tabs are strong, so dont worry about breaking them. Just be careful not to let it go flying and scratch up your paint.
Photo showing back of cover:
Step 2: that yellow wire leads to the puddle lamp. Remove the 2 screws from lower cover assembly. Next you need to pry off the lower cover. It's attached at several points, so the way I did it was wiggle it free on the right, then middle and then left and it came off pretty easily.
Photo showing back side of lower cover assembly, once removed from mirror housing.
Step 3: Twist the light socket from the lens assembly to reveal the old bulb and replace with your fancy new LED.
Reverse the process, reassemble and boom, LED puddle lamps.
Side note- taking this thing apart really explains all of the wind noise these things make while driving. There are no real seals or gaskets, so they just whistle dixie.
Hope this helps and let me know if you have any questions!