To prepare marinade, combine first 8 ingredients in a bowl; stir well with a whisk.
To prepare vegetables, working with 1 artichoke at a time, cut off stem to the base. Remove bottom leaves and tough outer leaves, leaving tender heart and bottom; trim about 1 inch from top of artichoke. Steam artichokes, covered, 20 minutes or until tender; cool to room temperature. Cut artichokes in half lengthwise. Remove fuzzy thistle from bottom with a spoon.
Steam potatoes, covered, 6 minutes or until tender. Cool to room temperature.
Trim carrot stems to 2 inches. Steam carrots, covered, for 20 seconds. Plunge into ice water; drain well.
Trim radish tops to 1 inch.
Place artichokes, potatoes, carrots, radishes, radicchio,and endive in a large bowl. Drizzle with marinade; toss gently to coat. Cover and marinate in refrigerator 2 hours.
Arrange vegetables on a platter; top with olives and cheese.
Wine Note: Serve the Baby Vegetable Antipasto and Rosemary-Scented Flatbread with Black Grapes with a light, snappy white like Pino and Toi from the producer Maculan. A blend of Pinot Grigio, Pinot Bianco, Tacai, and Chardonnay, the 2001 is $10. Other good bets: Italian Gavi or Orvieto.