Combine the cauliflower, carrots, celery, bell pepper, serranos, and garlic in a large bowl. Toss the vegetables until evenly distributed, then pack them tightly into four 1-pint jars with tight-fitting lids.

Bundle the dill in cheesecloth and tie it securely with kitchen twine. In a large saucepan over medium-high heat, combine the dill sachet, vinegar, water, sugar, and salt and bring to a boil. Once the liquid reaches a rolling boil, remove the pan from the heat and let the brine steep for 10 minutes to infuse the herbs. Discard the dill sachet.

Return the brine to a brief boil over medium-high heat, then pour it evenly over the vegetables in the jars, ensuring they are completely submerged. Allow the jars to sit at room temperature until cool to the touch. Cover the jars tightly and refrigerate for at least 7 days before serving—the vegetables need this time to fully pickle and develop their characteristic tang. The giardiniera will keep for up to 1 month.