Preheat the oven to 375°F (190°C). Place a rack in the center position.
If using an unbaked crust, fit it into a 9-inch pie dish. Line with parchment or foil and fill with pie weights (or dried beans). Blind bake for 10 minutes, then carefully remove the weights and liner.
In a large bowl, whisk together the eggs, heavy cream, whole milk, salt, pepper, and garlic powder until smooth.
Sprinkle the diced ham and shredded cheddar evenly over the crust. Add the green onions and chives (if using).
Pour the egg mixture over the filling. If the crust edges brown quickly, cover them with a pie shield or strips of foil.
Bake for 35–40 minutes, until the top is lightly golden and the center is just set (it should jiggle slightly but not slosh). A knife inserted near the center should come out clean.
Cool on a rack for 10 minutes before slicing and serving.