Slice onions into thin rings using the sharpest knife you have. Heat a large, heavy-bottomed pot or pan (cast-iron works wonders) over medium-high heat, then add the oil or butter. When hot, add onions, stir briefly to coat, lower heat to medium and leave alone for 15 whole minutes. After 15 minutes of not touching at all (don't even look at them), flip bottom layer to the top using a wide spatula. Cook for another 15 minutes without touching. When most of the onions are a deep golden-brown, stir mixture together, lower heat to lowest setting and continue to cook, stirring occasionally, until all onions are dark brown and completely caramelized, up to 15 more minutes.