Hopefully you're not bothering to core the top and the bottom of the onion; fussy, a waste of time, and works against his later goal of keeping the root intact while dicing.

I do it more or less this way - except I keep the root intact until the end. It keeps the onion structurally intact until I'm done with the dicing. At which point, the root takes a single chop to lop off, and then the whole thing scatters into tiny, mostly uniform dices. It's quite satisfying.

Chef Jean Pierre is the best, he explains so good that I really need to listen once to remember forever. Before discovering him, I wasn't interested in cooking at all and I listened to all the other chefs like Ramsay and Oliver but they don't tell you the complete story.

Why does he peel the oño like an orange when he’s about to cut it in half, why not cut it first?

Ah the famous oñyo video

Sorry, but I had to link to this video as you said "effectively": https://www.youtube.com/watch?v=eQgIwwKmjdo

I came up with this way by trial and error. Though I don't pare away the root. Just slice is off when dicing is done. Removing the roots helps a lot

This is silly. I’ve seen Indian street vendors do it the most efficient way. You tilt the knife with the front part down and the back maybe a quarter inch above the surface. That way as you slice the onion the little quarter inch holds it together as you turn it 90 degrees and make the perpendicular set of cuts.

That may be the most useful thing I've seen on the internet in months.

Thanks much!