Prepare the pressure canner, jars, and lids. You will need eight 1-pint jars or four 1-quart jars. Fill your canner with a few inches (about 8 cm) of water, depending on the instructions from your manufacturer, and place the canner on the stovetop over low heat with the jars inside to keep them hot. Heat the water to about 180 degrees Fahrenheit (82 degrees Celsius).
Put the oven on the broil setting, then coat the butternut squash cubes in oil and spread them on a baking sheet.
Broil the cubes in the oven until they are fully browned. This will take around five minutes.
Drain the water from the beans you soaked. Place them in a large stockpot and cover them with fresh water, then bring the beans to a boil.
Remove from the heat and drain the water.
Put the beans back in the stockpot on the stove. Add the roasted butternut squash cubes, along with the onions, carrots, broth, tomatoes, vinegar, spices, and garlic.
Bring the mixture to a boil over high heat, then reduce it to a gentler boil for about five minutes.
Take the stockpot off the heat. Then, ladle the soup into jars, putting the solids in evenly and using a bubble removal tool to get rid of any bubbles.
Check for headspace, aiming for about 1 inch (2.5 cm) of headspace.
If you find yourself short on liquid, add boiling water or hot chicken or vegetable broth.
Before putting the lids on the jars, wipe the rims with a clean, damp cloth. Place the bands and lids on the jars and load them into the pressure canner.
Process the jars at 10 lbs of pressure for 75 minutes (69 kPa) for 1-pint jars and 90 minutes for 1 quart jars. Adjust for altitude or for your manufacturer's instructions if necessary.
When the time has elapsed, turn the heat off and allow the canner to depressurize on its own. Then, remove the jars and allow them to cool for 12 hours before storing.