Preheat your oven to 350°F (180°C). Prepare a 9-inch (24 cm) pie dish and lightly grease it with olive oil to prevent the quiche from sticking.
Mash the peeled and cooked potatoes with a fork or potato masher. For a smoother consistency, use a hand mixer. Season with salt and pepper, and mix in 1 egg. This will be the \'crust\' base.
Spread the potato mixture evenly in the pie dish, shaping the edges as well. Use a spoon or your hands to create a uniform layer about 1 cm thick. Blind bake for 10 minutes to set slightly before adding the filling.
While the crust is baking, dice the onion, garlic, bell pepper, and zucchini. In a skillet, sauté them in olive oil for 5-6 minutes, until softened and their flavors have concentrated. If there's any excess liquid, let it evaporate.
In a bowl, whisk together the remaining 3 eggs, cream, grated cheese, salt, pepper, and nutmeg. This creamy mixture will give the quiche its rich flavor.
Stir the sautéed vegetables into the egg-cream mixture. Pour the entire mixture onto the pre-baked potato crust and spread it evenly.
Return to the oven and bake for another 30-35 minutes, or until the filling is set and the top is lightly golden brown. Check the center with a toothpick to ensure it's cooked through.
Once baked, let it cool for 10 minutes before slicing. Serve warm or cold; a side salad makes an excellent accompaniment.
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