Preheat the oven to 450°. Set a pizza stone on the bottom of the oven (alternatively, the pizza can be baked directly on the oven rack). In a large skillet, melt the butter in the olive oil. Add the onion and oregano sprig, cover and cook over moderately low heat, stirring occasionally, until softened, about 5 minutes. Add 2 tablespoons of water to the skillet and cook over moderate heat until the onion is caramelized, about 10 minutes; add a few tablespoons of water to the skillet if necessary. Add the balsamic vinegar and cook over moderate heat, stirring occasionally, until it has evaporated, about 10 minutes. Discard the oregano sprig and season the onion with salt and pepper.