Brandon says in the video, "The way you solve a 17 by 17 is just like you would a seven by seven, or a five by five. If you can solve one of those then the 17 by 17 isn’t that hard, but it is very, very tedious."
Here's the time lapsed video that let's you see the entire 7 hour process in under 7 minutes.
But if you have an entire work day to go through the intricate algorithms used in the solving of the cube, here you go: