How to Make It
In a medium saucepan, melt the butter in the olive oil. Add the onions and cook over moderate heat until softened, about 7 minutes. Add the water, balsamic vinegar, sugar and rosemary and season with salt. Cover partially and simmer over low heat until tender, about 30 minutes. Uncover the onions and simmer until the juices are syrupy, about 15 minutes longer. Discard the rosemary and serve warm.