In a medium bowl, whisk together the eggs, 2 tablespoons of chives and ½ teaspoon each salt and pepper. In a nonstick 12-inch skillet over medium, melt 2 tablespoons of butter. Add the mushrooms and cook, stirring occasionally, until well browned, 5 to 8 minutes. Stir in the wine and mustard, then cook, stirring, until the liquid has evaporated, about 2 minutes. Transfer to a small bowl and wipe out the skillet.