1. Place 2 to 3 tablespoons extra virgin olive oil (or half oil, half unsalted butter) in a heavy 10-inch skillet or pot over very low heat. Add 1 1/2 to 2 pounds sliced onions (1 pound of raw onions yields about 1 cup caramelized). The onions will be 2 to 3 inches deep; stir to coat with oil. Cover tightly and cook over very low heat, stirring occasionally, for 45 to 60 minutes, until completely softened and beginning to brown.
2. Increase the heat to medium; remove the lid and add 1 cup liquid (water, wine, or broth), scraping the pan to loosen any browned bits on the pan's bottom. Cook until the liquid evaporates and the onions are a deep caramel brown color.VARIATION: Quick Caramelized Onions
Cook sliced onions as in the preceding recipe, only increase the heat to medium or medium-high. Cover and stir often until the onions are softened and beginning to brown. Remove the lid; sprinkle the onions with 1 to 2 tablespoons granulated sugar, stirring to combine. Continue to cook until the onions are caramelized as desired.
VARIATION: Caramelized Onions Balsamico
Stir 1 to 2 tablespoons good quality balsamic vinegar into the caramelized onions; cook until liquid evaporates.

