Prepare: Prepare the canner, jars, and lids as outlined in the provided information. If you haven't already cut the veggies, make sure to wash, dry and cut the ingredients as listed.
Spice Bag: Create a spice bag by securing bay leaves, peppercorns, and garlic in a square of cheesecloth.
Make Pickling Brine: In a large stainless steel saucepan, combine vinegar, water, sugar, salt, (see NOTE 1) and the spice bag. Heat over medium-high heat until it reaches a boil. Stir to dissolve the sugar completely. Once boiling, lower the heat, cover the saucepan, and let it gently boil for about 5 minutes to infuse the liquid with the spices.
Heat Veggies: Add cauliflower, onion, celery, carrots, and zucchini to the mixture and bring it back to a boil. Remove the saucepan from heat and gently mix in the red, yellow, and green peppers. Don't forget to discard the spice bag.
Pack Jars: Pack the hot jars with the prepared vegetables, leaving about ½ inch of space from the top. Pour the hot pickling liquid over the vegetables, ensuring they are completely covered and leaving ½ inch of space at the top. Remove any air bubbles and adjust the headspace if necessary. Wipe the rim of the jars clean, then center the lid on each jar. Secure the jar lids by screwing the bands down until you feel resistance, and then tighten them with your fingertips.
Process: Place the jars into the canner, ensuring they are fully submerged in water. Bring the water to a boil and process the jars for 10 minutes (see NOTE 2 to adjust this time if you live >1000 feet above sea level/at high altitude). After processing, remove the canner lid, wait 5 minutes, and then carefully take out the jars. Allow the jars to cool before storing them.