Place the onion on a cutting board with the stem end pointing to the side. Holding the onion firmly with one hand, use a sharp chef's knife to slice off the stem end to create a flat surface.
Place the flat surface against the cutting board and slice through the root end from top to bottom.
Peel away and discard the skin, then place the cut sides down on the cutting board to minimize the fumes.
Take one half of the onion and make lengthwise cuts, slicing all the way to the root end (without slicing through the root itself). Adjust the angle of the knife as you slice, following the round shape. Move your fingers out of the way as needed, creating slices through the onion until you reach the end. The thinner the slice, the smaller the final pieces will be.
Next, make crosswise cuts, using your knuckles as a guide for the knife. Keep moving your guiding hand and fingers back, then grip the root as you come closer to the end.
Once the onion half is chopped, you can optionally run your knife through the pieces to make them smaller. Then repeat this process with the other half of the onion.
Use chopped onion immediately or store in the refrigerator, in an airtight container or resealable plastic bag, for 1-2 days.
See full post for step-by-step photos and additional tips.