Add the tomatoes to a blender or food processor. Pulse several times to crush the tomatoes.Transfer the tomato puree to a medium skillet set over medium heat. Stir in the brown sugar, lemon zest and juice, and ground ginger. Cook, stirring frequently, until the mixture is thick and jammy – this will take about an hour. (To test, dip a cool, metal spoon into the jam. It should slide of the spoon in a thick sheet – not in watery droplets.)Ladle the jam into the jars and seal. The jam is delicious right away, but tastes even better after a few weeks.