Cut mozzarella cheese into 24 thin sticks. Wrap each stick with 1 ham slice, and place in an 11- x 7-inch baking dish. Add tomatoes and next 3 ingredients.
Whisk together olive oil and next 6 ingredients. Drizzle over mixture in baking dish. Cover and chill 8 hours or up to 24 hours, turning occasionally. Drain and transfer to a serving dish.
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