Preheat oven to 400 degrees. Brush a 9-by-2 1/2-inch springform pan with 2 TBLS melted butter. Line the sides of the pan with strips of parchment paper, brush paper with butter. (Be generous on the bottom of the pan so the potatoes don’t stick) If you don’t have a springform pan, don’t worry, it works just as well in a 9″ pie pan and then you don’t need the parchment.
Squeeze excess moisture from hash browns. In a large bowl, mix thawed, drained hash browns with remaining butter, 1 egg, salt and pepper. Press hash brown mixture onto bottom and up the sides of your prepared pan. Press firmly to mold the potatoes against the edges. Place on a rimmed baking sheet; bake until set and the edges of the hash browns are lightly browned, about 20 to 25 minutes.
While the crust is baking, in a small skillet, sauté the pancetta until it’s crispy. Remove from skillet and drain on paper towels. Do not discard the bacon fat! Put red onions and garlic in the same skillet and sauté in the bacon fat until the onion is soft and the garlic is fragrant, about 3 minutes.
In a large bowl, whisk the remaining eggs and milk, then add the rest of the ingredients. Pour into prepared crust. Bake until set, 45 to 50 minutes. Let sit for 5-10 minutes to set completely. Carefully unmold Quiché,
Peel off waxed paper before serving.
Serve warm, at room temperature or cold.