1. Place racks in upper and lower thirds of oven and preheat to 350°F. Coat 2 24-cup nonstick mini-muffin pans with cooking spray. Place pans on foil-lined baking sheets. Scatter scallions and parsley over bottom of each cup.
2. Whisk eggs and yolks with Parmesan, salt and pepper in a large bowl. Whisk in milk until smooth. Transfer to a cup with a pour spout and fill each muffin cup with egg mixture. Top each cup with a pinch of Swiss cheese.
3. Bake until quiches are puffed and browned on top, about 30 minutes, rotating pans from top to bottom racks and turning back to front about halfway through.
4. Immediately run a small, sharp knife around outside of each quiche, then invert onto a wire rack to cool. Turn each quiche right side up. Serve warm or at room temperature.