Heat olive oil in a medium saucepan over medium-high heat. Add onion and garlic and cook until fragrant. Add tinned tomatoes and cook, stirring, until sauce is simmering. Gradually stir in tomato paste and cook uncovered for 15 minutes or until sauce reduces.
Turn down heat slightly and add flaked tuna. Stir in parsley then gradually add balsamic vinegar to taste. Season to taste and serve hot over cooked pasta with grated parmesan.