Place cauliflower, bell peppers, and carrots in an eight-quart pot half full of unsalted boiling water, then immediately turn off heat and let stand, uncovered, two minutes. Drain vegetables in a colander and spread out on a kitchen towel to cool to room temperature

Bring remaining ingredients to a boil in a three-quart nonreactive saucepan over moderate heat, stirring until sugar is dissolved.

Transfer this pickling liquid to a four-quart nonreactive bowl and cool to room temperature, about 30 minutes. 

Discard garlic (don’t be alarmed if it has turned blue in reaction to the vinegar) and add vegetables to pickling liquid. Weight vegetables with a plate to keep them submerged in liquid if necessary. Chill, covered, at least one week.