Prepare your jars, lids, rings, and canner.
Wash your jars, lids, and rings in hot, soapy water.
Fill the pressure canner with 2-3 inches of water and put it on the stove on a low heat to warm.
Put a little water in the clean jars to keep them weighed down, and place them in the canner.
Turn the canner off when it begins to steam to keep the jars warm.
Fill jars, fit lids, and place in pressure canner.
Remove the hot jars from the canner and turn the canner on again to bring the water to a low simmer (180°F).
Use a funnel to fill the jars with asparagus soup, leaving 1 inch of headspace. Release the bubbles, adding more liquid if needed.
Clean the rims of the jars with a vinegar-soaked towel and gently screw on the lids to fingertip tight.
Carefully place the jars into the pressure canner.
Place the lid on the pressure canner and turn up the heat.
Let the steam vent for 10 minutes.
Put the pressure regulator on the lid.
Bring the canner to 11 PSI on a dial gauge or 10 PSI for a weighted gauge (adjust for elevation).
Once your canner has stabilized at full pressure, set a timer for 60 minutes for pint jars (75 minutes for quarts).
Turn off the heat, then let the canner come down to 0 PSI by itself.
Remove the pressure regulator and let the canner stabilize for 5 minutes before removing the lid.
Carefully take the lid off the canner.
Remove the jars and set them on a clean towel where they can cool undisturbed for 16-24 hours.
Check each seal, remove the bands and clean jars with room-temperature water, if needed.
Label each jar with the contents and year.
Store the jars out of direct sunlight.