Set a large saucepan over medium-high heat and add vinegar, water, sugar, salt, garlic, bay leaves, black peppercorns, mustard seeds, coriander, and crushed red pepper flakes. Bring the pickling brine to a simmer and stir until all sugar and salt have dissolved, then shut off heat.
Firmly pack shredded cabbage and carrots into large mason jars, then pour the hot brine over the top until filled, dividing the seasonings between the jars. Seal with lids and store in the refrigerator at least overnight for the best flavor, then enjoy.
When kept refrigerated, you can expect your pickled cabbage to last for weeks.
Notes
Expect a small cabbage to yield 6-8 cups of shredded cabbage.