1. Sterilize jars, and prepare lids.
2. While jars are boiling, toss together first 4 ingredients and 3 tsp. salt in a very large bowl. Let stand 20 minutes. Drain.
3. Bring vinegar, sugar, remaining 1 tsp. salt, and 2 cups water to a boil in a 12-qt. stainless steel or enameled stockpot, stirring until sugar dissolves.
4. Place 1/2 tsp. pickling spice, 1/2 tsp. mustard seeds, and 1 garlic clove in each hot jar. Using a slotted spoon, transfer vegetables to hot jars, packing tightly and leaving 1/2-inch headspace. Cover vegetables with hot pickling liquid, leaving 1/2-inch headspace. Seal and process jars, processing 15 minutes.
5. Remove jars from water, and let stand, undisturbed, at room temperature 24 hours. To check seals, remove the bands, and press down on the center of each lid. If the lid doesn’t move, the jar is sealed. If the lid depresses and pops up again, the jar is not sealed. Store properly sealed jars in a cool, dark place up to 1 year. Refrigerate after opening.