Prepare boiling water canner. Heat jars in simmering water until ready for use. Do not boil. Wash lids in warm soapy water and set aside with bands.

Bring water to a rapid boil in stockpot. Working quickly to prevent browning, peel and remove ends from eggplants. Cut into sticks approximately 3 inches long and 3/4 inch wide. Immediately add to stockpot and return to a boil. Reduce heat and boil gently for 10 minutes, pressing the eggplant under the water every 2 minutes to remove air, until eggplant is tender. Transfer to a colander placed over a sink and rinse with cold running water to stop the cooking process. Let drain for 1 minute without pressing out excess liquid. Set aside.

Combine in a large stainless-steel saucepan, white vinegar, balsamic vinegar, sugar, oregano and salt. Bring to a boil over medium-high heat, stirring to dissolve sugar. Add eggplant and return to a boil. Remove from heat.

Place 1 clove garlic in each hot jar. Pack hot eggplant into hot jars to within a generous 1/2-inch of top of jar. Ladle hot pickling liquid into jar to cover eggplant, leaving 1/2-inch headspace. Remove air bubbles. Wipe the jar rim. Center the lid on the jar. Apply the band, and adjust to fingertip-tight. Place the jar in the boiling-water canner. Repeat until all the jars are filled.

Water must cover jars by 1 inch. Adjust heat to medium-high, cover canner, and bring water to a rolling boil. Process pint jars 15 minutes, adjusting for altitude. Turn off heat and remove cover. Let jars cool 5 minutes. Remove jars from canner; do not retighten bands if loose. Cool 12-24 hours. Check lids for seal, they should not flex when center is pressed.