Prepare the pressure canner, jars, lids, and bands. Put the trivet in, add 2 to 3 inches of water following your manufacturer's directions, and bring the canner to a gentle simmer with the jars warming inside it.
Peel the potatoes, carrots, and onions, then cut them to a uniform size. Trim the beef and cut it into 1-inch cubes.
Combine the beef, potatoes, carrots, peas, onions, water, broth, thyme, garlic powder, and salt in a large stockpot.
Bring the mixture to a boil, then reduce the heat and simmer 10 minutes. The vegetables will not be cooked through, which is correct, since they finish cooking in the jars.
Take the stockpot off the heat and divide the mixture among the hot jars, loading the solids first and then ladling broth over them, leaving 1 inch headspace.
Release trapped air bubbles, then check the headspace again and top up with hot broth or boiling water to hold 1 inch.
Wipe the rims and threads clean, set the lids on, and apply the bands fingertip tight.
Load the jars into the pressure canner, fasten the lid, and vent a steady stream of steam for 10 minutes before adding the weight or closing the petcock.
Process pints for 75 minutes or quarts for 90 minutes at 10 pounds pressure in a weighted gauge canner or 11 pounds in a dial gauge canner, adjusting for altitude (see notes).
Turn off the heat and let the canner depressurize on its own, then wait 5 minutes before removing the lid, opening it away from your face.
Leave the jars in the canner another 10 minutes, then remove them to a towel lined counter and let them cool undisturbed for 12 hours.
Check the seals, remove the rings, label the jars, and store them in a cool, dark place.