Slow-cook - Stir together chopped onions, olive oil and salt in a heavy stainless steel pan. Cover, and cook over the lowest possible heat setting for 30 minutes, stirring occasionally. Be careful not to let the onions color. (If needed at any point, stir in just enough water to moisten the onions.)
Caramelize - Uncover, andsauté onions on medium-high heat until deeply caramelized to golden brown, about 30 minutes.Frequently scrape the brown glaze from the bottom of the pan with a wooden spoon or metal spatula, being careful not to let the onions, nor the glaze on the bottom of the pan, burn.(Lower the heat if necessary. If just a small area of the glaze on the bottom of the pan starts to char, pour a spoonful of water directly over it and, using the wooden spoon, quickly rub it with the onions to dissolve it.)
Cover and let the onions sit undisturbed off the heat for 5 minutes. Then uncover and stir the deeply flavorful glaze detached from the pan into the onions.
Storing - Tightly seal. Keeps up to 3 days in the refrigerator, or 3 months in the freezer.
Tools
Quality heavy-bottomed stainless steel saute pan or pasta pan