Preheat oven to 350°F (180°C).
Gently wipe the mushrooms with a wet sponge, then slice. Use the stems too. Peel and slice the onion. Peel and grate the garlic. Cut the bacon into approx. 1/3 inch / 1 cm pieces.
If using fresh broccoli, cut the florets into smaller pieces first, then blanch them until a bit al dente 2-4 min. for smaller florets, and 4-5 min. for medium ones. If using frozen broccoli, cook 2 min. less than package directions, as they will be finished in the oven, and then cut into smaller florets.
Drain the broccoli in a colander and rinse with cold water to stop the cooking. If using frozen broccoli, try to squeeze out as much water as possible, without destroying the florets. Just gently squeeze them between your palms.
Melt the butter in a pan on medium-high heat. Add the bacon and cook until nice and a bit crispy. Then, remove it to a small bowl. Add the onions, and sauté until softened. Add the garlic and the mushrooms, and cook until they start to soften, but still hold their shape. Don't cook too much, or they will start to release water. Add the spinach and cook for a few seconds, until it wilts down a bit.
In a medium-sized bowl, prepare the egg filling. Whisk together the eggs, milk (cream if using), salt, pepper and nutmeg (optional). Then add the grated Parmesan cheese.
Place the pastry sheet in a 9-inch (25 cm) tart pan with detachable bottom, going all the way up the sides of the pan. Then pass a rolling pin over the pan, removing the excess pastry. Poke the pastry on the bottom and sides with a fork.
Transfer the mushroom mixture and bacon, into the tart pan, making sure everything is evenly spread out all over. Arrange the spinach evenly; the colors should be evenly distributed, so the quiche will look pretty once baked. Then, nicely arrange and spread out the broccoli florets on top. Slowly pour egg mixture covering the veggies. Arrange some mushroom slices on top for visual appeal.
Bake at 350°F (180°C) for 45-55 minutes (but check at 30 min.). The quiche is ready when it has a darker golden brown color on top, but the middle is just slightly jiggly when you shake it.
Remove from the oven and let cool for 10-15 minutes in the pan, so the egg filling has time to set, then place on a wire rack and let cool completely.
Serve on its own or with a salad or some protein on the side. Either way, this quiche is absolutely delicious and impressive. Enjoy!