Prepare the vegetables: Wash and chop the cauliflower, carrots, celery, red bell pepper, and garlic. Slice the green olives and set them aside.
Make the brine: In a medium saucepan, bring the water to a boil. Add the salt and stir until fully dissolved. Remove from heat and let it cool to room temperature.
Pack the jar: In a large, clean glass jar, layer the prepared vegetables, packing them tightly to prevent air pockets. Add in the mustard seeds, coriander seeds, and red pepper flakes. Pour in the optional apple cider vinegar if using.
Pour the brine: Once the brine has cooled, pour it over the vegetables in the jar, ensuring everything is fully submerged. You can place a small weight (such as a clean rock or another jar) on top to keep the vegetables submerged under the brine.
Ferment: Cover the jar loosely with a lid or cloth, allowing air to circulate while preventing debris from getting in. Leave the jar at room temperature for 3-5 days, tasting daily to check the flavor and fermentation. The giardiniera will get more tangy as it ferments.
Store: Once it reaches your desired tanginess, transfer the jar to the refrigerator to slow the fermentation process. It will keep for several weeks in the fridge.