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.