In a large sauté pan, heat the olive over moderate heat. Add the onions or leeks, carrots, celery (including leaves), any other optional vegetables and salt and sauté for about 5 minutes. Turn down the heat to low and simmer, partially covered, until very soft, 30 minutes or longer, stirring occasionally. If the mixture dries out while cooking, add up to ¼ cup of water.
Stir in the parsley and simmer for another 5 minutes, partially covered.
Remove from the heat and allow to cool. Purée in a food processor or blender to form a thick paste. This may take several minutes.
Store as much as you'll use for the week in the refrigerator and freeze the rest by arranging tablespoon-size scoops on a cookie sheet, placing the sheet in the freezer and once frozen, transferring the blobs to a container and returning them to the freezer.
To make vegetable broth, for every 1 tablespoon of vegetable base, add 2 cups of very hot water.