Preheat oven to 400°F. Lightly grease a 9x13-inch baking dish.
Roll out the pie crust as needed to fit the bottom and about 1 inch up the sides of the dish, pressing it gently into the corners. Trim off any excess.
Lightly dock the crust with a fork and blind-bake for 8-10 minutes, just until it starts to look dry and slightly set. Let cool slightly.
Place the pancetta in a skillet over medium heat and cook, stirring occasionally, until the fat has rendered and the pancetta is browned and crisp, 6-8 minutes.
Transfer to a paper towel–lined plate to drain and cool slightly.
Scatter the cooked pancetta evenly over the bottom of the crust. Sprinkle the green onions, thyme, and chives evenly over the pancetta.
Top with the cheddar and Gruyère, spreading both cheeses in an even layer.
Crack the eggs into a large liquid measuring cup or bowl. Add enough half-and-half so that the total volume reaches 2 cups. Whisk until well combined and slightly frothy.
Whisk in the salt, pepper, cayenne, and nutmeg.
Carefully pour the custard over the filling, stopping when the custard is just below the top edge of the crust. If you have a little extra custard, discard it or save for a small ramekin, rather than overfilling.
Bake at 400°F for 10 minutes, then reduce the oven temperature to 350°F without opening the door. Continue baking until the center of the quiche is just set, slightly puffed, and only a gentle wobble remains, about 25-35 minutes more.
If the crust or top browns too quickly, tent loosely with foil during the last 10 minutes.
Transfer the quiche to a rack and let cool for at least 10-15 minutes so the custard finishes setting and slices cleanly.
Slice into squares and serve warm or at room temperature.