Position an oven rack in the bottom third of the oven and preheat it to 425 degrees F. Generously grease a 9-inch springform pan with butter.
Toss the hash browns with the butter in a large bowl until well coated. Evenly press the hash browns into the bottom and up the sides of the prepared pan. Bake until deep golden brown and crispy, 40 to 45 minutes. Reduce the oven temperature to 350 degrees F.
Meanwhile, whisk the eggs and half-and-half in a large bowl until combined. Fold in the cheese, chives, ham, 1 teaspoon salt and a few grinds of black pepper. Pour the egg mixture into the potato crust and bake until the eggs are set, 40 to 45 minutes more.
Let cool in the pan for 10 minutes. Run a knife around the edge of the pan, unmold the quiche and transfer to a serving plate or cutting board.
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