Spray 2 heavy baking sheets with non-stick spray. Arrange onion wedges in a single layer on the baking sheets and dot with 4 tablespoons of butter. Season with salt and pepper. Bake until onions are dark brown, stirring once or twice – about 40 minutes.
While onions are baking, boil broth in a large, heavy skillet over high heat until reduced to about ½ cup, about 6-8 minutes. Add sugar and vinegar and cook, stirring, until sugar dissolves and the mixture comes to a boil.
Add the onions to the sauce, reduce heat to medium-low. Simmer until the liquid is reduced and syrupy, about 5 minutes. Season with salt and pepper. Can be prepared 1 day ahead. Cover and refrigerate. Reheat over low heat or in microwave.