Trim the cauliflower into bite-sized florets (about 1 ½ inches), and discard the tough stems.
Peel the ginger and turmeric with a vegetable peeler, and slice them into thin, matchstick pieces.
Trim the stems off the chiles and slice them in half lengthwise. Leave the seeds and membranes in if you like more heat. Alternatively, cut the chiles into thin strips.
Place the vinegar, water, garlic, salt, and sugar in a large saucepan. Stir well so the salt and sugar are combined, and bring it to a boil. Reduce the heat and simmer for 5 minutes. Turn off the heat and let the brine cool for about 10 minutes.
Place the ginger, turmeric, chilis, and cauliflower into the hot brine. Stir it and let it sit for 10 minutes or until you can insert a sharp knife into the cauliflower, but it's still firm.
Using a ladle or slotted spoon, transfer the vegetables to a glass bowl with a lid, or a gallon jar with a lid. Pour enough hot brine over the vegetables to submerge everything. Discard any extra brine.
Store in a covered container in the refrigerator for up to 3 weeks. The vegetables should be ready to eat within 24-48 hours, but they taste better the longer they sit in the brine.