Preheat the oven to 375°F.
Add the butter and oil to a 12-inch cast-iron skillet set over medium-high heat.
Once the butter has melted and the mixture is hot, add the hash browns, 1/2 teaspoon salt and 1/4 teaspoon pepper and stir to combine then using the bottom of a dry measuring scoop, press the potatoes into an even layer on the bottom and up the sides of the skillet.
Cook the potatoes until they begin to brown and crisp on the bottom, occasionally pressing them as needed to compact the crust, 7 to 10 minutes. While the potatoes are browning, make the filling.
Place the thawed spinach in a towel and ring out as much liquid as possible.
In a large bowl, whisk together the eggs with the half-and-half, 1/2 teaspoon salt and 1/2 teaspoon pepper.
Stir in the spinach, ham, cheese and chives.
Remove the skillet from the heat.
Pour the egg mixture on top of the potatoes then transfer the skillet to the oven. Bake the quiche until the eggs are set and no longer jiggly, 35 to 40 minutes.
Remove the quiche from the oven, allow it to cool for 15 minutes, then slice and serve.