Over-under coiling is the only way
Yes, the over-under method — also called “figure-eight” coiling — is the right way to store extension cords.
The common mistake is wrapping the cord around your elbow in a big loop. That twists the wires inside each time you flip the cord over your hand. Over time, those twists become kinks, then breaks.
The over-under technique alternates the twist direction with each loop. One loop goes over your hand (clockwise), the next goes under (counter-clockwise). This cancels out the twisting. The cord lies flat when you pull it out, no tangles, no internal damage.
Practice it three times. You’ll feel stupid for about ninety seconds, then it clicks. After that you’ll never go back.
Side note: If you’re storing a very long cord (100ft+), consider a cord reel instead. But for 25-50 foot cords, over-under is faster.