Begin by preparing the canning jars for use. Fill a large pot with water and bring it to a simmer. Submerge the canning jars in the simmering water for at least 5 minutes to sterilize them thoroughly. Meanwhile, wash the lids and rings in warm soapy water and set them aside to dry.

In a large pot, combine the apple cider vinegar, white sugar, salt, mustard seed, dried basil, cinnamon, and black pepper. Stir the mixture well and bring it to a gentle boil over medium heat, ensuring all the sugar is dissolved. This typically takes around 5 minutes of stirring.

Once the sugar has dissolved, add the finely chopped green tomatoes, red bell peppers, red onion, celery, and Granny Smith apples to the pot.

Stir the mixture thoroughly to combine all the ingredients. Allow the mixture to come to a vigorous boil, stirring occasionally, and let it cook until the vegetables and apples have softened and the flavors have melded together. This usually takes about 15 to 20 minutes.

While the piccalilli mixture is cooking, carefully remove the sterilized canning jars from the simmering water using tongs or a jar lifter.

Fill each jar with the hot piccalilli mixture, leaving about 1/4 inch of space at the top. Use a knife or spatula to remove any air bubbles and wipe the rims of the jars clean with a damp paper towel.

Place the washed lids on top of each jar and screw on the rings securely, but not too tightly. This allows air to escape during the canning process, ensuring a proper seal.

Set a rack in the bottom of a large stockpot and fill it halfway with water. Bring the water to a boil. Using a jar lifter, carefully lower the filled jars into the boiling water, making sure there is at least 2 inches of water covering the jars. Boil the jars for about 10 minutes to process them.

After processing, carefully remove the jars from the boiling water and place them on a clean towel or wooden surface to cool completely. As the jars cool, you may hear the lids "pop," indicating a proper seal.

Once cooled, check the seals by pressing down on the center of each lid. If the lid is firm and doesn't move, it's sealed correctly. Store the sealed jars in a cool, dark place for future use.