This will keep up to a month in the fridge in a tightly sealed container. Substitute balsamic for the banyuls vinegar if you don't have it:
Lemon-Onion Jam
1/4 cup olive oil
1/2 cup sugar
4 cups onions, large dice
1/2 cup Banyuls vinegar
1/2 tsp. caraway seed
1/2 tsp. fennel seed
2 Tbsp. Lemon Zest
2 Tbsp. Lemon Juice
Kosher Salt and Fresh Cracked Pepper to taste
Method:
In large saucepan, heat oil over medium heat until hot. Stir in sugar, then cook, stirring constantly with wooden spoon, until mixture turns a light caramel brown, about 10 minutes. Add onions, salt and pepper, then cook for 15 minutes, stirring frequently, to brown and cook onions. Add vinegar, lemon juice, fennel, and caraway seed and stir well to mix. Simmer over medium heat for 30 minutes until mixture combines and thickens. Stir in lemon zest. Cool completely. Store in a tightly sealed container in the refrigerator.