In a large, heavy-bottomed pot, heat olive oil over medium-high. Add onions and cook, stirring often until golden brown, about 15 minutes. Reduce heat to low and add herb sprigs. Cook another 3 minutes, stirring often.
Evenly sprinkle sugar over the onions and cook without stirring until the sugar melts, about 5 minutes (if sugar is disturbed by stirring or shaking, it will seize into clumps and require more time to melt). Increase heat to medium-high and cook untouched until it becomes an amber-colored caramel, about 6 minutes — watch closely and reduce heat if caramel begins to burn.
Stir in the vinegar and cook another 5 minutes or so. It’s fully thickened when a spoon across the bottom of the pan separates the jam for several seconds. Discard herb sprigs and season with salt to taste. Cool, then transfer to a sealed container. Store in fridge for a week or freezer for 3 months. Serve warm or at room temperature.
NOTE: Onion jam pairs well with pork, chicken, and lamb, or add to a charcuterie board, pizza, crostini, or grilled cheese.
Per serving: 130 calories, 4 grams fat (0.5 gram saturated fat), 0 milligrams cholesterol, 28 milligrams sodium, 23 grams total carbohydrates, 2.5 grams fiber, 1 gram protein.
