1. Preheat the oven to 350ºF and grease a non-stick muffin tin.
2. Heat oil in a medium skillet, over medium low heat. Add the shallots and saute until tender, about 2 minutes. Add the broccoli and season with salt and pepper then cook until tender crisp, about 3 to 4 minutes. Remove from the heat and set aside allowing the broccoli mix to cool a bit.
3. In a medium bowl, whisk the eggs, milk and Dijon mustard. Stir in the cheeses.
4. Evenly divide the broccoli mixture between the prepared muffin tins and then pour the egg mix in each; filling them about two-thirds of the way up. If you’d like, sprinkle the tops with a bit more Parmesan cheese.
5. Bake in the oven for 25 to 30 minutes, or until the tops are golden brown and the center of the cups are set.
6. Remove from the oven and allow them to cool for a few minutes and then loosen the quiche from the cups and pop them out. Serve warm or store them in an airtight container.