- Add flour and salt to a food processor. Blend for a few seconds. Add butter and blend for a few seconds at a time until butter is the size of peas. Add the egg, water, and Parmesan. Mix until the dough starts to take shape. Remove dough from food processor and shape into a disc. Wrap dough and refrigerate for 30 minutes.
- Place rack in the middle of the oven. Preheat the oven to 200°C (400°F).
- Heat 30 mL (2 tbsp.) butter in a 25-cm (10-in.) non-stick, ovenproof skillet and brown mushrooms over high heat. Set aside on a plate. In same skillet, heat remaining butter over medium heat and fry onions and garlic for 15 minutes or until softened and coloured.
- Add the reserved mushrooms, balsamic vinegar, Parmesan, and parsley. Season with salt and pepper. Set aside.
- On a floured work surface, roll out the dough into a 25-cm (10-in.) round.
- Top mushroom mixture with dough. Bake in the oven for 20 minutes, or until crust is golden brown. Turn over and out onto a serving dish.
If you don't have this type of non-stick skillet, transfer the mushroom mixture into a 25-cm (10-in.) pie pan and top with dough.
Serve the tarte tatin at cocktail hour, or as a main dish accompanied by an arugula salad with shaved Parmesan.