In a food processor, purée half the tomatoes with chilies, garlic, ginger and tamari. In a medium pot on high heat, pour in tomato mixture, along with brown sugar and red wine vinegar and bring to a boil, stirring occasionally. When it boils, lower heat and simmer gently for 10 minutes.
Dice and add in the remaining tomatoes, and add balsamic vinegar. Gently simmer for another 10 minutes, stirring every 3 minutes to release solids that settle on the bottom. Scrape the sides of the pot during cooking so mixture cooks evenly.
When it’s cooked down, pour warm jam into a clean glass jar with lid and allow to cool to room temperature. Store in refrigerator up to 2 weeks.
Tip: As with relishes, chutneys and other jams, this can be stored without refrigerating if you are familiar with preserving and canning procedures.