Prepare the pie crust by rolling out the chilled pie dough on a floured surface. Transfer to a 9-inch pie pan, pressing the dough into the edges. Trim any excess dough and refrigerate for at least 30 minutes.

Preheat oven to 375°F (190°C). Line the chilled crust with parchment paper and fill with pie weights or dried beans. Bake for 15-20 minutes until edges are slightly golden.

Remove pie weights and parchment. Brush the crust with two separated egg whites and return to the oven for 5-7 minutes until fully cooked.

In a mixing bowl, whisk together the two whole eggs and two egg yolks. Gradually add heavy cream and whole milk, mixing until creamy. Season with kosher salt and black pepper.

Sprinkle chopped ham across the bottom of the pre-baked crust, followed by Gruyère cheese and sliced chives. Pour the egg mixture over evenly.

Bake assembled quiche for 30-35 minutes until puffed and lightly golden with a gentle jiggle in the center. Cover with foil if the top browns too quickly.

Let the quiche cool on a wire rack for 10-15 minutes before slicing. Serve warm or at room temperature.