Preheat the oven to 375 degrees F (190 degrees C).
Melt butter in a skillet over medium heat. Saute onion and ham in the melted butter until onions are soft and ham begins to brown, 8 to 10 minutes. Remove from the heat and set aside to cool.
Whisk eggs, milk, garlic powder, salt, and pepper together in a large bowl.
Evenly spread corned beef hash onto the pie crust, pressing firmly with the back of a spoon. Spread ham and onion mixture over top. Pour egg mixture over the top until filled; avoid overfilling. Top with Cheddar cheese.
Place the quiche on a cookie sheet and bake in the preheated oven until crust is golden brown and center is set, 25 to 30 minutes. Remove from the oven and let stand for 10 minutes before slicing. Serve warm.
You can use any cheese in place of Cheddar.
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