Heat a nonstick saucepan for a moment, add the chopped tomatoes, and stir them over medium heat until all the liquid evaporates, about 5 minutes, turning up the heat for the last minute.
Prepare an ice bath.
Add the capers, ginger, and garlic and cook another minute. Put the mixture in the bowl set in ice to stop the cooking. When just cool, stir in the oil, salt, and pepper. Let sit 1 hour. Adjust the seasoning and serve at room temperature.
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