Place the tomatoes in a food processor and process until coarsely chopped.
Heat a large heavy-bottomed soup pot at medium-high heat. Add the olive oil and garlic and sauté for 1 minute only. Add the tomatoes and reserved tomato juice and bring to a boil. As soon as the sauce reaches boiling point, reduce heat to medium to medium-low and simmer uncovered for 40 minutes to 1 hour (depending on how watery your heirlooms are) until the sauce has thickened and the tomatoes separate from the olive oil, stirring from time to time. Add the basil, salt, pepper and balsamic. Continue to simmer for 2 to 3 minutes until basil has wilted. Remove from heat and transfer to a bowl to cool, or proceed with your recipe of choice.
Cook’s note 1: Refrigerate up to 3 days or freeze up to 2 months.
Cook’s note 2: If making several batches of the recipe, decrease the olive oil by half and increase the cooking time to about 30 minutes for each additional portion.
Example: If you multiply the recipe 3 times, use 9 lbs tomatoes, 3/4 cup oil and simmer the sauce for 1 hour and 40 minutes to 2 hours. All other ingredients in the recipe can be multiplied exactly 3 times. Last but not least, you’ll need to increase the heat as it’ll take more heat to keep a good simmer going with this much sauce.