Be sure to choose a heavy-bottomed skillet with a light interior—it will make it easier to monitor the browned bits in the bottom of the pan to avoid scorching the onions.
Peel the onions. Halve and slice lengthwise into uniform pieces (about 3/8-inch-wide slices are ideal, but a little larger or smaller is fine).
Heat oil in a 10- to 12-inch high-sided skillet over medium-high. Add half the onions; turn to coat. Cook until sizzling, about 2 minutes. Add remaining onions in handfuls, folding with tongs to coat in oil. (Pan will be very full at this point).
Cook onions, tossing often with tongs, until hot and sizzling, about 3 minutes. Add salt (to help draw moisture out of the onions), and toss to combine.
Cover, reduce heat to medium, and cook until onions have collapsed to half their height and a pool of liquid has collected in bottom of skillet, about 10 minutes
Fold onions with a spatula, scraping bottom of pan to ensure they don’t stick or scorch. Cook, stirring every 5 to 6 minutes and reducing heat as necessary to maintain a gentle simmer, until liquid has evaporated, about 35 minutes.
When pan looks dry, increase heat to medium, and scrape bottom and sides of pan with a rubber spatula, shaping mound of onions into an even patty pulled away from edges of pan. This careful shaping will help the onions cook evenly and prevent scorched bits around the edges.
If onions start to stick to bottom of pan, or if fond on bottom of pan darkens more quickly than the onions, add a splash of water, and stir and scrape to loosen any browned bits. Stir onions well until they are uniform in color, and reshape into a patty.
Continue cooking, stirring, splashing in additional water, and reshaping into a patty as needed, until onions are the color of bourbon, 35 to 45 minutes. Remove onions from pan, and use as desired.