Prepare your pressure canner, jars, lids, and bands according to the manufacturer’s instructions. Wash the jars well and keep them hot until needed.
Peel the potatoes and cut them into cubes. Slice the carrots, chop the celery, dice the onion, and mince the garlic. If the beef is not already cut, trim it as needed and cut it into about 1 1/2-inch cubes.
Heat the olive oil in a large heavy-bottomed pot or Dutch oven over medium-high heat. Add the beef and brown it on all sides, working in batches if needed so the meat browns properly instead of steaming.
Once all the beef is browned, return it all to the pot if you worked in batches. Add the potatoes, carrots, celery, onion, and garlic, and stir everything together.
Add the salt, thyme, pepper, and beef stock. Save the bay leaves for adding individually to each jar. Stir well, then bring the mixture to a boil over medium-high heat.
Once boiling, reduce the heat and simmer the stew for about 5 minutes until heated through.
Ladle the hot stew into hot quart jars, making sure each jar gets a balanced mix of meat, vegetables, and broth. Slip one bay leaf in each jar. Leave 1 inch headspace.
Use a bubble remover or nonmetallic utensil to remove air bubbles from each jar. Add more broth if needed to maintain the proper 1 inch headspace.
Wipe the jar rims with a clean damp cloth, then apply the lids and bands, tightening the bands to fingertip tight.
Place the filled jars into the prepared pressure canner. Lock the lid, vent the canner for 10 minutes, then bring it up to pressure.
Process quart jars for 90 minutes at 11 pounds pressure in a dial gauge canner or 10 pounds pressure in a weighted gauge canner, adjusting pressure as needed for altitude.
When the processing time is complete, turn off the heat and allow the canner to return to zero pressure naturally. Do not force cool the canner.
Once the canner is fully depressurized, wait a few minutes, then carefully remove the lid. Let the jars rest in the canner for about 5 minutes before removing them.
Transfer the jars to a towel-lined counter and let them cool undisturbed for 12 to 24 hours. Check the seals, remove the bands for storage, label the jars, and store them in a cool, dark place.