Wash your hens, making sure there are no residual feathers, organs or packing materials remaining.
Place all ingredients except sea salt inside 1 or 2 cotton mesh bags, pull or tie them closed, and place them so they sit low in your stockpot. (You can buy Soup Socks for this purpose as well.) Alternately, you can strain your broth with a china cap when it is done.
Fill the stockpot or slow-cooker with fresh spring or filtered water, making sure the hens are fully submerged. Add salt and then vinegar, if using. Cover.
Bring to a boil, then turn down to simmer for 3-5 hours. I simmer longer for better gel. If you are using a slow-cooker, put it on high for 2-3 hours, then on low for 6-8 hours, though test it the first time, because slow-cookers can really vary.
After the broth has cooled a bit, remove the ingredient bags/Soup Socks and empty them into a large bowl. The chickens will completely fall apart. Separate the meat from the skin, sinews and bones and set aside to use in soup, salads, or other dishes, as you wish.
Once the pot has cooled enough to lift, start transferring the broth to Mason jars for storage in the freezer and fridge. If you like your broth particularly clear, you can strain it again through cheesecloth as you fill your jars.
If you plan to freeze your broth, leave at least an inch of room in the jar for expansion, so your jars don't break.
Check your broth after a day in the fridge to see how well it gelled! The thicker the better. You may also have a nice, yellow layer of chicken fat (schmaltz) on top, which you can skim to cook with, or stir into soups and sauces, as you like.
To add a nutritional boost and a deeper flavor to your dishes, use your broth wherever you might use water to cook veggies, meats, beans or grains.