In a small saucepan, make a brine by bringing the vinegar, water, sugar, salt, black peppercorns, mustard seeds, celery seeds, coriander seeds, and red pepper flakes (if using) to a boil. Reduce the heat and simmer for 10 minutes, and then remove the pan from the heat and set aside.
Cut the carrots, cucumbers, peppers, and cauliflower into 1-inch / 2.5 cm chunks, slicing the carrots and cucumbers on an angle. Save the tops of the peppers; they look lovely facing out here and there in the jar. Trim the green beans and leave them whole.
Place the cucumbers in a colander in the sink with 2 cups of ice cubes for 30 minutes; this enhances their crunch. Pack 2 pint jars or 1 quart / 1 L jar tightly with the vegetables, garlic cloves, and dill. Ladle the brine into the jars to cover the vegetables, with 1?2- inch / 1.5 cm headspace.
Cover the jars with their lids and refrigerate. The pickles are ready to eat as soon as the next day, but gain flavor over time. They’ll keep in the refrigerator for a couple of weeks.