In a 5- to 6-quart pan over high heat, bring broth and rice to a boil. Reduce heat and simmer, stirring occasionally, until rice is just tender to bite, 13 to 15 minutes. Drain rice; reserve broth for other uses, or discard. Pour rice into a shallow 11- by 17-inch pan and spread level. Let cool, stirring occasionally, about 20 minutes.
Meanwhile, stack ham slices and cut into strips 1/4 inch wide and 1 inch long. Rinse and drain tomatoes, basil, and capers. Cut tomatoes in half and basil leaves into slivers; peel and mince garlic.
In a large bowl, mix ham, tomatoes, basil slivers, capers, garlic, and olive oil. Add cool rice, mix gently, and season to taste with salt and pepper. Garnish with basil sprigs.