Let the pie crust soften at room temperature until it is ready to roll.
On a lightly floured surface, roll the pie dough into a 13-inch circle, about ⅛-inch thick. Press the dough into a 9-inch pie plate. Trim any uneven edges, leaving a 1-inch overhang. Tuck the overhang under and press the crust to the rim of the pie plate. Crimp the crust with your fingers or as you like. Place in the freezer for 20 minutes.
While the crust is chilling, preheat the oven to 425°F.
Press a piece of parchment paper inside the crust to fully cover it, then fill it with pie weights or dry baking beans. Bake for 10 to 12 minutes until the edges of the crust look dry.
Remove the weights and paper. Poke the crust 10 to 12 times all over with the tines of a fork. Return to the oven for 6 to 8 more minutes until the inside looks dry and the crust is lightly golden. Let the crust cool while you make the filling. Reduce the oven temperature to 350°F.
In a medium bowl, whisk together the eggs, cream, milk, salt, and pepper. Stir in ¾ cup ham (135g), ¾ cup cheese (75g), and the green onion. Pour the egg mixture into the prepared crust. Place on a rimmed baking sheet.
Bake for 30 minutes. Sprinkle the top of the filling with the remaining ¼ cups of ham (45g) and cheese (25g). Continue baking for 20 to 25 minutes more or until the filling is puffed and completely set.
Cool for 30 minutes before slicing and serving. Garnish with additional thinly sliced green onion, if desired.
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Notes
Pat the diced ham very dry before adding it to the filling. Too much moisture can keep the filling from setting properly. If time allows, I recommend you also cook the ham in a dry skillet over medium heat for 5 to 6 minutes, stirring frequently, until it releases some liquid and is lightly browned. Let it cool slightly before adding to the filling.
If you want to use "wet" ingredients for your mix-ins, do what you can to remove excess moisture first. This means cooking raw veggies until the pan is dry or squeezing out excess liquid from ingredients like defrosted frozen spinach or grated raw potatoes (though not frozen hash browns—they're already pressed).
If you are cooking a filling, make sure to let it cool after cooking so you don't accidentally scramble or curdle the custard mixture when you add it.
Use a pastry mat with measurements to help you roll out the dough to the appropriate size for your pie plate.
If the edges of your pie crust are browning too quickly, tent them with foil or use a pie shield.
Let the quiche rest for a full 30 minutes before slicing. Otherwise, they won't be as clean or sturdy, and the filling may ooze out.