Prepare your pressure canner, jars, lids, and bands according to the manufacturer's instructions. Keep jars hot until needed. Cut the beef chuck into 1 to 1.5 inch cubes. Dice the onion, slice the carrots and celery, cube the potatoes, mince the garlic, and slice the mushrooms.
Heat the olive oil in a large heavy-bottomed pot over medium-high heat. Brown the beef in batches without crowding the pan, adding more oil as needed. Browning in batches builds a deep fond in the pan that gives the finished broth its richness. Set the browned beef aside.
In the same pot, cook the onion, carrots, celery, and garlic until softened. Add the mushrooms and cook for a few minutes until they begin to release their liquid. Return the browned beef to the pot. Add the red wine, beef stock, potatoes, bay leaves, thyme, parsley, pepper, and salt. Stir well and bring to a boil. Reduce heat and simmer for 5 minutes until everything is heated through.
Remove and discard the bay leaves. Use a slotted spoon to distribute the solids evenly between the hot jars, then ladle the broth over the top to 1 inch headspace. If you run short on broth, add a bit of boiling water or additional stock. Remove air bubbles, wipe rims, and apply lids and bands to fingertip tight.
Load jars into the preheated pressure canner. Lock the lid, vent for 10 minutes, then bring to pressure. Process pints for 75 minutes and quarts for 90 minutes, adjusting pressure for altitude. Allow the canner to depressurize naturally. Remove jars and cool on a towel-lined counter for 12 to 24 hours. Check seals, label, and store in a cool dark place.