What's the best way to cook very large chicken breast filets?
It really depends on what types of meals you plan to make with them.

If you would typically serve people a whole breast, then I'd cut each one down into more reasonable sizes (slice vaguely across the grain ... I usually start at the more bulbous end and slice diagonally through it so I end up with a chunk that's mostly from the thin end)

For the size you're starting with, you might want to cut each one into 4 to 6 pieces.  If you're planning on pounding them, I might even go with 8 to 10 pieces.

Once they're a more reasonable size, you can then brine and bake them or pound them out, them like you normally would.

As you mention boiling them ... I would recommended poaching them instead.  If you cut them up first, go with my original recommendation of an hour.  If they went in whole, I might give it two hours.  The technique that I mention is more like a slow cooker -- it's more forgiving and doesn't tend to overcook the outside before the middle is done  (although, it can get fall-apart tender, and start breaking up as you try to fish them out with tongs.