Prepare the short pastry. Wrap tightly in plastic and refrigerate for 30 minutes, or up to a day.
Steam the broccoli florets for 7 minutes, until cooked but still firm. Set aside in a colander. In a medium mixing bowl, whisk together the milk, cream, and eggs. Season with salt, pepper, and nutmeg.
Remove the dough from the fridge and let stand at room temperature for 10 minutes. Preheat the oven to 350 degrees F. Grease a 10-inch ceramic quiche pan with olive oil. Working on a lightly floured surface, roll out the dough in a 12-inch circle. Transfer the dough into the pan, prick the bottom all over with a fork, and press on the sides with your fingers so the dough will adhere. Bake for 7 minutes, until lightly golden.
Peel, quarter, core, and dice the apple. Remove the pan from the oven (leave the heat on). Arrange the broccoli, apple, and cheese in the tart shell. Pour in the milk mixture and bake for 35 minutes. Turn the oven off and leave the quiche in the closed oven for 10 more minutes, until the filling is set.
Transfer the pan to a rack to cool for 5 minutes. Serve warm, with a mache salad. You can make the quiche a few hours or a day ahead and reheat it for 15 minutes in a 350 degrees F oven to revive the crispness of the crust.