• 4 chicken livers, cut into pieces
Put 3 tablespoons of the oil in a medium skillet over medium-high heat; a minute later, add the onion and cook, stirring, until it begins to brown, about 5 minutes. Meanwhile, beat the eggs with about half the cheese and some salt and pepper.
Add the sage and livers to the onion and cook, stirring occasionally, until pink, about 3 minutes. Pour in the eggs and vermouth and stir until the eggs set, a minute or so. Garnish with the remaining olive oil and Parmesan and serve hot, warm or at room temperature.