Set up the pressure canner by filling it to the line inside the pressure canner with water.
Sterilize the jars, lids and bands, then set them aside.
Put the oil into a large cast iron skillet and turn the heat on medium.
Brown the stew meat in small batches and once it is browned, transfer it to a large stainless steel stock pot.
Once all the meat is in the stock pot, add the potatoes, carrots, salt, pepper and thyme to the stock pot and then cover all the ingredients with boiling water.
Bring the contents of the stock pot to a boil, stirring frequently.
Ladle the hot stew into the hot canning jars making sure to leave one inch of headspace.
Wipe the rim of the jars with a paper towel moistened with vinegar.
Place the lid on the jar and then the band.
Tighten the band until resistance is met and then tighten it a little more until it is finger-tip tight.
Place the jars in the pressure canner.
Lock the lid and bring the canner to a boil over medium heat.
Vent the steam for 10 minutes, then place the weight, set to 10 pounds pressure on the vent.
Use the instructions that came with your canner so you know when you reach the 10 pounds of pressure.
Process pint jars for 75 minutes and quart jars for 90 minutes.
When the timer goes all, turn off the heat, but do not move the canner or open it*. Let the pressure return to zero naturally.
Wait 2 minutes after the pressure returns to zero naturally and then remove the weighted gauge from the vent and also remove the canner lid.
Let the jars sit in the bottom of the canner for an additional 10 minutes.
Then remove the jars, tighten the bands and let them sit overnight.
The next day, remove the bands to check the seals.
If the lids are sealed, label and date the jars, then store them in a cool, dry place.
If the lids are not sealed, start back at step 8 and reprocess the jars or put them in the refrigerator to be eaten right away.
Notes
*Attempting to open a pressure canner before the pressure returns to zero naturally can cause them to explode.