Prepare jars. Clean jars with hot, soapy water. Prepare your pressure canner by adding 3 inches of water to the bottom (or as much water as your pressure canner manufacturer recommends). Add a splash of white vinegar to the canner. Place the clean jars in the pressure canner with water inside so they don’t float around. Set the burner to medium heat and allow the jars to heat up. Add the lids and rings to a small pot over medium-low heat and allow them to simmer. Do not boil.
Cook the meat. Add the oil to a large pot over medium heat. Once the oil warms, add the stew meat. Cook the stew meat for 3-5 minutes or until it browns on all sides.
Add vegetables. Next, add the potatoes, carrots, celery, onion, and garlic. Stir to combine. Add enough water to cover the mixture.
Add herbs. Add the salt, oregano, basil, rosemary, parsley, and pepper. Stir to combine. Bring the mixture to a boil, stirring often.
Boil water. Bring a separate pot of water to a boil. Later, this will be used to fill the jars back up.
Fill jars. Once the meat and vegetable mixture has come to a boil, ladle it into the hot jars, leaving a generous 1-inch headspace. (Cooking the vegetables down is unnecessary since they will be while the jars are processed.)
Remove bubbles. Remove the bubbles from the jars using a debubbler, a plastic knife, or a wooden chopstick.
Prepare jars. Fill the jars back up with boiling water (from that separate pot earlier) so they have a 1-inch headspace. Clean the rims of the jars with a clean, moist towel. Place the lids and rings on the jars, tightening them until they are fingertip-tight.
Process jars. Transfer the jars to the pressure canner, and adjust the water level to your manufacturer’s recommendation. Place the lid on and lock it. Set the burner to medium-high heat. Allow the canner to vent steam for 10 minutes continuously. After 10 minutes, set your canner to 10 pounds of pressure. Once it hits 10 pounds of pressure for weighted (or 11 pounds for dial gauge), set your timer for 75 minutes for pints (or 90 minutes for quart jars) (adjusting for altitude). Do not start the timer until your gauge is at pressure. If the gauge drops below 10 pounds of pressure, increase the heat and start the timer over. The jars need to be processed at the correct pressure the whole time. Turn off the heat. Turn off the heat and allow the pressure to come down naturally. Once the gauge reads 0 pounds of pressure, you can remove the weight or reduce the dial to zero. Allow the canner to release more pressure. Wait five more minutes after the pressure is fully released before removing the lid.
Cool the jars. Remove the lid, tilting it away from your face, and allow the jars to sit in the canner for 10 more minutes. Transfer the jars to a heat-safe area to cool for 12-24 hours. After 24 hours, check the seals. If you have confirmed a proper seal, you can store the jars for 12-18 months or per your manufacturer’s lid recommendations.