Hull and cut the tomatoes into a rough dice. If you're using heirloom tomatoes, be sure to cut off any tough, brown spots that might be on their skin. Transfer the chopped tomatoes to a non-reactive medium pot, along with the brown sugar, salt and red wine vinegar. Place the uncovered pot over medium heat and bring the mixture to a simmer; cook for 30 minutes. At the 30 minute-mark add the dried thyme and mix. Cook for an additional 25 to 30 more minutes and until the mixture is thick. If you're using more or less tomatoes, the cook time will definitely vary.

Allow to cool to room temperature. Transfer to a jar and store in the refrigerator. Tomato jam will be good for two weeks without canning.