Position rack in center of oven; preheat to 325°F. Coat a nonstick muffin tin generously with cooking spray (see Tip).
Heat a large nonstick skillet over medium-high heat. Add sausage and cook until golden brown, 6 to 8 minutes. Transfer to a bowl to cool. Add oil to the pan. Add mushrooms and cook, stirring often, until golden brown, 5 to 7 minutes. Transfer mushrooms to the bowl with the sausage. Let cool for 5 minutes. Stir in scallions, cheese and pepper.
Whisk eggs, egg whites and milk in a medium bowl. Divide the egg mixture evenly among the prepared muffin cups. Sprinkle a heaping tablespoon of the sausage mixture into each cup.
Bake until the tops are just beginning to brown, 25 minutes. Let cool on a wire rack for 5 minutes. Place a rack on top of the pan, flip it over and turn the quiches out onto the rack. Turn upright and let cool completely.
A good-quality nonstick muffin tin works best for this recipe. If you don't have one, line a regular muffin tin with foil baking cups.