To begin, melt butter and olive oil in a large skillet over medium-low heat. Add the chopped onions and sprinkle kosher salt over them. Cook gently, stirring occasionally, for about 40 to 50 minutes until the onions turn a beautiful light golden brown. Be patient; the longer they cook, the sweeter they become. If they start browning too quickly, reduce the heat.
While the onions are caramelizing, preheat your oven. Arrange your oven rack in the bottom third and place a baking stone or a metal baking sheet on the rack. Preheat the oven to 375 degrees Fahrenheit.
Next, prepare your pie pan by lightly brushing a 10-inch deep dish pie pan with melted ghee. Drape one sheet of phyllo dough into the pie pan, ensuring it covers the sides. Brush it lightly with more melted ghee focusing on getting a thin layer on the bottom. It’s important to keep the remaining phyllo covered while you work to prevent it from drying out.
Continue layering the remaining phyllo sheets, rotating them slightly each time for even coverage. Once all sheets are in place, brush the final layer generously with melted ghee and fold the edges over the top, brushing them again with a bit more ghee.
To prevent the crust from puffing up, place a weight in the bottom of the crust. You can use a smaller pie pan, parchment paper with pie weights, or even a chain designed for baking. Place the pie pan on the preheated stone or baking sheet and bake for about 10 minutes, or until the edges just start to color. Remove the weight and bake for an additional 2 to 3 minutes to dry out the bottom.
Once the crust is lightly baked, allow it to cool slightly while you prepare the filling. Reduce the oven temperature to 350 degrees Fahrenheit.
In a blender, combine the eggs, whole milk, heavy cream, and crème fraîche. Blend on low until smooth. Mix in the additional kosher salt, black pepper, and nutmeg. If you prefer, you can whisk these ingredients by hand, ensuring they’re well combined.
Scatter the caramelized onions evenly in the bottom of the par-baked crust, followed by about 1¼ cups of your chosen cheese. Pour the egg mixture gently over the top, then sprinkle the remaining cheese for an extra cheesy finish.
Bake the quiche in the oven for 45 to 55 minutes. You want the edges to be browned and puffed, with the center just slightly jiggly. To check for doneness, insert a paring knife near the center; it should come out cleanly. If the edges start to brown too much, cover them gently with a ring of foil.
After baking, remove the quiche from the oven and let it cool on a wire rack for 1 to 2 hours. For the best results, refrigerate it (covered) for a few hours or overnight to allow it to fully set before slicing. Reheat slices by placing them on a baking sheet and baking at 350 degrees Fahrenheit for 5 to 10 minutes until warmed through and the crust is crispy again.