Prepare boiling water canner. Heat jars in simmering water until ready to use, but do not boil. Wash lids in warm soapy water, and set aside with bands.
In a saucepan over medium heat, simmer white vinegar, sugar, turmeric, peppercorns and salt for five minutes. Lower heat just to keep brine hot.
Place carrots, cauliflower, dill sprigs and garlic inside jars, leaving a ½-inch headspace. Carefully pour hot brine over vegetables in jar, maintaining the ½-inch headspace. Remove air bubbles, and wipe jar rim. Centre lid on jar, apply band, and adjust to fingertip tight. Place jar in canner. Repeat until all jars are filled.
Ensure jars are covered by at least one inch of water. At altitudes up to 1,000 feet, cover canner and process jars at a full rolling boil for 20 minutes.
Turn off heat, remove canner lid, and let jars stand five minutes. Remove jars from canner, and cool undisturbed at room temperature 12 to 24 hours. Check lids for seal; they should not flex when centre is pressed.
Store jars for at least one month before using for best results.