In a large skillet over medium heat, caramelize the onions in the butter until tender and golden brown. Add salt and pepper to taste. Add the balsamic vinegar, lower the heat and cook until the vinegar thickens, about an hour. Add the syrup and cook until the mixture thickens again, about another hour.
Serve at room temperature. Store the jam in the refrigerator for up to 1 week.
Recipe courtesy of The Fabulous Beekman Boys