Roll the chilled pie dough into a large round on a lightly floured surface. Press it into a pie dish, trim the edges, and crimp the rim. Place it in the refrigerator to chill thoroughly.
Preheat the oven and line the crust with parchment paper, filling it with pie weights or beans. Bake until the edges are set, then remove the weights, prick the base, and continue baking until lightly golden. Reduce the oven temperature afterward.
Cook the bacon in a skillet until crisp, then transfer to paper towels and chop into small pieces.
In the same skillet, melt butter and cook the diced onion until soft and lightly caramelized. Set aside to cool slightly.
In a large bowl, whisk together the eggs, cream, milk, cornstarch, salt, pepper, cayenne, and nutmeg until smooth. Stir in the chives if using.
Spread the cooked onions over the baked crust, followed by half of the bacon and all of the cheese. Add the remaining bacon, then pour the custard mixture over the top.
Place the quiche on a baking sheet and bake until the center is set and the top is golden. If it browns too quickly, loosely cover with foil while finishing baking.
Allow the quiche to rest before slicing so the filling sets properly.