Half of Earth with most landmass
You would have to cut somewhere along this circle:



The only landmass here is New Zealand, eastern Australia, eastern PNG, western North America and some Pacific islands. I'm pretty sure you can tweak it a bit, but that's the basic idea.
Notice that this actually shows less than a half because of the relatively low altitude. If you "zoom out" infinitely you'll get some more Australia and more America in this, but it's still going to be mostly ocean.