I found myself looking for a faster way to chop up a bunch of apples this week, and serendipitously figured out this easy way to core apple halves.
You'll need a cutting board, a knife, and a melon baller.
Cut your apple in half. Pull off the stem. Place half your apple stem-side down on your cutting board (this keeps it more stable).
Grab your melon baller and push it through the core area. Empty the melon baller as it fills with core. You might have to make two passes.
Ta-da! A nice, tidy apple half all ready for slicing.
I used the sliced apples to make apple nachos. We all liked them!