Thoroughly scrub the potatoes and cut away any green spots or blemishes.
Peel them, making sure the peels are at least ¼ inch thick.
Set the peeled potatoes aside for another recipe.
In a large stockpot, combine the potato peels, quartered onion, sliced carrots, celery, water, parsley, oil, bay leaf, thyme, sage, and garlic clove(s). For the Garlic Broth variation, add the entire head of garlic cloves now and ensure you are using olive oil.
Bring the mixture to a boil, then reduce the heat to a gentle simmer.
Cover partially and let it cook for 1½ to 2 hours, until the vegetables are very soft and the broth is a fragrant, light brown color. If the liquid evaporates too much, add a little more water to keep the vegetables submerged.
Taste the broth. If it seems weak, continue to simmer uncovered to reduce and concentrate the flavor. If it's too strong, add a splash of water.
Season generously with salt and pepper to your liking.
For a clear broth, carefully strain the liquid through a fine-mesh sieve into a large bowl or container, discarding the solids.
For a thicker, purée-style soup base, remove the bay leaf and celery stalk.
Then, press the remaining vegetables and broth through the sieve to extract more body and flavor.
Finish the broth with a final flavor boost. A few drops of hot sauce or a squeeze of fresh lemon juice can brighten and enhance all the savory notes.
Keep a bag in your freezer for other vegetable scraps like onion ends, carrot peels, and celery bottoms to add to your next batch for extra complexity.
Freeze leftover broth in ice cube trays. These flavor cubes are perfect for deglazing a pan, thinning a sauce, or adding a savory boost to grains.
Don't be afraid to simmer the broth longer if it tastes weak. Reducing the liquid is key to concentrating the flavors into a rich, delicious stock.