Spread a kitchen towel on the counter. Remove a warm jar from canner using the jar lifter. Drain the water back into the canner and place on the towel. Keep the remaining jars in the canner so they stay hot.
Use the canning funnel and fill the jar with the sliced jalapeños.
Ladle hot pickling liquid over the peppers and maintain a 1/2-inch headspace.
Run the bubble popper through the jars to release air bubbles. Wipe the rim clean with a damp paper towel.
Center a lid on the jar, and screw on the band until it is fingertip tight. Use the jar lifter to place the jar back into the canner, and repeat with the remaining jars.
Once jars are all in canner, adjust the water level so it is two inches above the jar tops.
Cover the canning pot and bring it to a rolling boil over medium-high heat. Once the pot boils, process half-pints for 10 minutes at altitudes of less than 1,000 ft. Adjust processing time for your altitude if necessary. (See notes)
When processing time is complete, turn off heat, remove the cover by tilting lid away from you so that steam does not burn your face, and allow the canner to cool down and settle for 5 minutes.
Spread a dry kitchen towel on the counter. Use a jar lifter to remove the jars one at a time from the canner. Keep the jars upright, and place them on the towel. Do not tighten ring bands or test the seals yet. Let the jars sit undisturbed for 12 to 24-hours to cool.
After the jars have cooled for at least 12 hours, check to be sure lids have sealed by pushing on the center of the lid. The lid should not pop up. If the lid flexes up and down, it did not seal. Place the jar in the refrigerator, and use within a month.
Remove the ring bands, wash, label, date the jars, and store in a cool, dark place between 50 to 70 degrees F for 12 to 18 months. Allow 4-5 weeks for the pickles to develop flavor. Once the jar is open, refrigerate and use up within a month. Makes about 5 half-pint jars of picked jalapeños.