Rinse the dried navy beans and remove any damaged beans or debris.
Cover the beans with several inches of water and soak overnight (12–18 hours).
Drain and rinse the soaked beans.
Place the beans in a large stockpot and cover with fresh water. Bring to a boil and simmer for 30 minutes. Do not fully cook the beans.
While the beans simmer, combine the chicken broth, ketchup, brown sugar, molasses, maple syrup (if using), apple cider vinegar, Worcestershire sauce, dry mustard, smoked paprika, onion powder, garlic powder, black pepper, salt, and liquid smoke in a large pot. Bring to a gentle simmer and stir until the sugar dissolves.
Drain the partially cooked beans and add them to the sauce. Simmer together for about 30 minutes so the flavors blend.
Prepare your pressure canner, jars, lids, and bands according to the manufacturer's directions.
Fill hot jars about three-quarters full of beans, then ladle the hot sauce over them, leaving 1 inch of headspace. Remove air bubbles and adjust headspace if needed.
Wipe the jar rims, apply the lids, and screw on the bands until fingertip tight.
Process in a pressure canner according to your altitude:Half-pints and pints: 75 minutesQuarts: 90 minutes Allow the pressure canner to depressurize naturally. Remove the jars and let them cool undisturbed for 12–24 hours.
Check that each lid has sealed before labeling and storing the jars in a cool, dark place.