Preheat the oven to 350 degrees. Cut each tomato in 3 pieces. In a mixing bowl, toss the tomatoes with the garlic, shallots, 1 tablespoon Tantillo California Extra Virgin Olive Oil, and the Dijon mustard.
Place the mixture in a shallow baking dish and roast for 30 minutes. (In the summer months, put the mixture in an aluminum foil pouch and place on the grill for a smoky flavor. Let cool for 20 minutes.)
Transfer the mixture to afoot processor and puree. Add the Tantillo Balsamic Vinegar and basil and mix.
Season with salt and pepper to taste.
While mixing, slowly drizzle in the remaining 3 tablespoons Tantillo California Extra Virgin Olive Oil to form an emulsified mixture.
Refrigerate for up to 3 days.