Step 1 Cut off the stem and root ends of the onions, then halve them lengthwise and peel away the dried brown skin. Cut the onions lengthwise into one-fourth inch thick slices. As you finish, gather the onions in a large, heavy-bottomed pot (preferably cast-iron). A 7-quart pot will work just about perfectly.
Step 2 When all of the onions have been sliced, pour over the oil and the salt and stir to combine. Set over medium heat and cover. Cook until the onions begin to wilt, stirring every 10 to 15 minutes to keep from sticking. As the onions soften, they will reduce in size quite dramatically.
Step 3After 20 to 30 minutes, the onions will be quite soft and they will begin to stick to the bottom. Reduce the heat to low and continue cooking with the pot covered, stirring every 10 to 15 minutes to keep from sticking.
Step 4After 45 to 50 minutes, the onions will be silky and will be swimming in moisture. Remove the lid and increase the heat back to medium. Cook, stirring frequently, until the moisture has mostly evaporated and the onions have begun to turn golden, about 25 to 30 more minutes.
Step 5Once again, reduce the heat to low and continue cooking, stirring every 15 to 20 minutes, until the onions really begin to brown more deeply, about 2 more hours (this will make 2 1/2 to 3 hours total).
Step 6At this point, you'll need to watch the onions very carefully, stirring every couple of minutes or so. Cook until the onions have been reduced to a deep, reddish-brown marmalade, watching that they do not dry out, about 1 more hour, making 3 to 4 hours total.