Heat olive oil and butter in a saucepan over medium-low heat. Stir in the onion, and cook until it has caramelized to a dark, golden brown, about 15 minutes. Stir in the balsamic vinegar, and cook for 1 minute before stirring in the chicken bouillon and cream. Bring to a simmer, then remove from the heat and stir in the Parmesan cheese until melted.
