Smash the shallots using the flat side of a large knife.
Combine the sugar, 1 cup of water, the vinegar, wine, and salt in a large saucepan over low heat. Stir to dissolve the sugar. Add the shallots, bay leaves, and thyme. Raise heat to medium-high and bring to a boil. Reduce heat to a simmer and cook, stirring occasionally, for about 1 1/2 hours or until the shallots are translucent and the liquid has been reduced to a syrup.
Remove from heat and cool before serving. (You may cover and refrigerate the jam for up to 2 weeks.) Serve cold or at room temperature.