Start by preheating your oven to 350°F (175°C). This ensures that the quiche cooks evenly.
In a sauté pan, heat 1 tablespoon of extra-virgin olive oil over medium heat. Add the sliced shallots and cook until they are translucent, about 3-4 minutes. Then, add the broccoli florets and water. Cover and cook for an additional 3-5 minutes until the broccoli is bright green and tender. Once done, remove from heat and let it cool slightly.
In a mixing bowl, whisk together the 6 large eggs, 1 cup of milk, 1 teaspoon of sea salt, and a few grinds of black pepper. Ensure everything is well combined and fluffy.
Once the broccoli and shallots have cooled, mix them into the egg mixture along with the grated Gruyere cheese and fresh thyme or chives. Stir until everything is evenly distributed.
Lightly grease your pie dish with a bit of olive oil to prevent sticking.
Pour the egg and vegetable mixture into the prepared pie dish. Bake in the preheated oven for 35-40 minutes, or until the quiche is set and lightly golden on top. You can check for doneness by inserting a toothpick in the center; it should come out clean.
Let the quiche cool for about 5-10 minutes before slicing. This allows it to firm up a little, making it easier to cut. Serve warm, and enjoy!