Wash and stem tomatoes. Cut the tomatoes into quarters and remove seeds over a mesh strainer. Reserve the juice.
Place the tomatoes in a big baking dish or 9 x 13 pan. Add roughly chopped onions, peeled garlic, and basil leaves to the pan.
Pour the reserved tomato juice over the tomatoes, onion, and garlic. Sprinkle all with salt and freshly cracked pepper. Drizzle with olive oil and toss to coat all the tomatoes.
Roast at 400° for 45 minutes, stirring halfway through the cooking time. Remove and cool for about 10 minutes.
Drain about a cub of the liquid off and then pour the remainder in batched to a food processor. Be sure to leave an inch in the processor bowl. Blend to a fine texture. Add balsamic vinegar. Blend one more time.
Taste for your desired saltiness. Add more salt if needed.