Combine all ingredients in a very large stockpot and cover with just enough water to cover the vegetables (about 3 quarts).
Bring it up to a boil over medium-high heat and then lower the heat to let the liquid simmer, continuing to cook, adding more water to keep the veggies covered, for at least 1 hour and up to 1-½ hours.
Let the broth cool until it is easier to handle. Remove the veggies with a slotted spoon, and then strain the remaining broth through a fine-mesh strainer. You may want to strain twice!
Pour broth into storage containers and let cool completely before covering. Broth can be stored in the refrigerator for up to 5 days. If the broth is unused after 5 days bring it to a boil before using. You can also add salt here to taste, before storing, or add as using.