Step 1: Peel and thinly slice the onions. In a large, heavy-bottomed pot, melt the butter over medium heat and add the onions.
Step 2: Cook the onions, stirring occasionally, for 45-60 minutes until they are a deep, dark mahogany brown. If they stick, add a splash of water to deglaze.
Step 3: Add the minced garlic and cook for 2 more minutes until fragrant.
Step 4: Pour in the sherry or wine to deglaze the pan, scraping up all the browned bits from the bottom.
Step 5: Add the beef broth, balsamic vinegar, thyme, bay leaves, salt, and pepper. Bring the mixture to a boil, then reduce heat and simmer for 10 minutes.
Step 6: Prepare your pressure canner and jars. Ensure jars are clean and warm.
Step 7: Ladle the hot soup into jars, leaving 1 inch of headspace. Ensure each jar gets a fair share of onions and broth.
Step 8: Wipe the rims with vinegar, apply lids and rings, and process in a pressure canner. Process pints for 60 minutes or quarts for 75 minutes at 10 lbs of pressure (adjust for altitude).
Step 9: Allow the canner to depressurize naturally before removing jars. Let them sit undisturbed for 24 hours to ensure a proper seal.