Preheat the oven to 375 degrees F (190 degrees C) and lightly coat a 12-cup nonstick muffin pan using cooking spray.
Add the oil to a large nonstick skillet and saute the shallot, mushrooms and a little salt and black pepper until the mushrooms are lightly browned and the shallots are soft.
This will take about 10 minutes.
Remove from the heat and add the nutmeg and spinach. Stir for a couple of minutes, then let the mixture cool for 5 minutes.
Whisk the eggs with the egg whites and milk, adding a pinch each of salt and pepper.
Stir in the cheese, then divide the mixture between the muffin cups.
Don't fill them more than halfway.
Top with the spinach mixture.
Bake for 20 minutes or until the quiches are golden brown and set, and have risen.
Allow them to cool in the pan for 5 minutes then transfer them to a wire rack and delight in the fact you now know exactly how to make vegetable quiche.
You can serve them warm or at room temperature.