Preheat the oven to 375°F (190°C).
Roll out the pie crust and fit it into a 9-inch pie dish.
In a mixing bowl, whisk together the eggs, milk, salt, pepper, and nutmeg.
Evenly distribute the diced ham and shredded cheese over the crust.
Pour the egg mixture over the ham and cheese.
Bake the quiche for 35-40 minutes, or until the filling is set and lightly browned.
Remove from the oven and let it cool for 5-10 minutes.
Garnish with fresh parsley before serving.
Cut into wedges and serve warm or at room temperature.
Enjoy your delicious ham and cheese quiche!