In a large stockpot, melt the butter with olive oil over medium heat. Add the sliced onions and stir to coat. Sprinkle with salt and sugar to enhance caramelization. Cook the onions, stirring occasionally, until they become golden brown and caramelized, about 45 minutes.

Pour in the white wine to deglaze the pot, scraping up any browned bits from the bottom. Allow the wine to simmer until it's reduced by half, intensifying the flavor.

Add the beef broth, bay leaves, and dried thyme to the pot. Bring the mixture to a boil, then reduce the heat and let it simmer for 30 minutes, allowing the flavors to meld together beautifully. Season with freshly ground black pepper to taste.

While the soup is simmering, prepare your pressure canner according to the manufacturer's instructions. Sterilize the canning jars and lids to ensure they're clean and safe for use.

Remove the bay leaves from the soup. Using a ladle, fill each sterilized jar with the hot soup, leaving a 1-inch headspace at the top. This space is crucial for proper sealing and expansion during processing.

Run a bubble remover or a non-metallic spatula around the inside of each jar to release any trapped air bubbles. This step helps prevent air pockets that could affect the seal and storage.

Wipe the rims of the jars with a clean cloth to remove any residue. Place the lids on top and screw on the bands until they're fingertip tight. Avoid over-tightening, as air needs to escape during processing.

Place the filled jars into the pressure canner. Process them at 10 pounds of pressure for 1 hour and 15 minutes, adjusting for altitude as necessary. Proper processing ensures the soup is safe for long-term storage.

After processing, carefully remove the jars using a jar lifter and place them on a towel-lined surface. Allow them to cool undisturbed for 12 to 24 hours. Once cooled, check the seals by pressing the center of each lid; it should not flex up and down. Store sealed jars in a cool, dark place.