I found a lot of forum posts where people were asking how to replace the glass, but there were no good answers for any Hyundai model. I even found a few online service manuals, but they didn't show how to get the glass backing bracket out. As it turned out, it was very easy to replace, but I could only get a good look at the bracket once it was off the car. Since there was no information on either replacement option, I wrote up instructions for both.
Step 1: Order Parts
One place where I did find OEM glass for a good price was www.newhyundaiparts.com. Their price is $70.03 for the bare glass or with the mounting bracket.
I also found a whole side mirror replacement on Ebay for $58.40. Since I couldn't find good instructions to get the bracket out and it was by far the cheapest option, I went ahead and bought this one. This part is clearly not OEM, but there is no obvious difference between them but the mold numbers.