Bring a large saucepan of water to a boil. Place a large bowl of ice water next to the stove. Cook carrot, cauliflower and green beans in the boiling water, one vegetable at a time, until just tender, 1 to 3 minutes. Transfer the vegetables to the ice water with a slotted spoon as they are done.
Drain the vegetables and place in a large, shallow nonreactive bowl (see Tip). Add fennel, bell peppers, hot peppers, celery and onion.
Combine cider vinegar, white vinegar, 1/2 cup water, sugar, salt, celery seed, basil and oregano in a nonreactive saucepan. Bring to a boil, then simmer for 2 minutes. Pour the hot liquid over the vegetables and gently stir to coat. Let cool to room temperature, stirring occasionally, then refrigerate until cold, at least 1 hour. The longer the vegetables marinate, the more flavorful the salad will be.
To serve, strain the vegetables (reserving the pickling liquid). Return the vegetables and 3 tablespoons of the pickling liquid to the bowl. (Reserve the remaining pickling liquid to pickle more vegetables or to use in a salad dressing, if desired.) Add garlic, olives, parsley, dill and oil to the vegetables; toss to combine. Season with pepper.