In a sieve over a medium non-reactive saucepot, strain the tomatoes of their juice into the sauce pot. Add the sherry vinegar, sugar, red pepper flakes, oregano, and basil to the tomato juice. Stir and cook over high heat. Once bubbles begin to form on the surface, reduce to a simmer. Allow liquid to reduce by 1/2 or until liquid has thickened to a loose syrup consistency. Squeeze each tomato thoroughly to ensure most seeds are removed. Set the tomatoes aside.
Cut carrot, onion, and celery into uniform sizes and combine with olive oil and garlic in a non-reactive roasting pan over low heat. Sweat the mirepoix until the carrots are tender and the onion becomes translucent, 15 to 20 minutes. Add the tomatoes and capers to the roasting pan.
Place roasting pan on the middle rack of the oven and broil for 15 to 20 minutes, stirring every 5 minutes. Tomatoes should start to brown slightly on edges with light caramelization. Remove the pan from the broiler. Place the pan over 2 burners on the stove. Add the white wine to the tomatoes and cook for 2 to 3 more minutes over medium heat. Put the tomatoes into a deep pot or bowl and add the reduced tomato liquid to the tomatoes. Blend to desired consistency and adjust seasoning