Preheat the oven to 450 degrees F. Slice the potatoes lengthwise into thin ovals (use a mandoline if you have one). Toss with the olive oil and season with salt and pepper, then arrange in a single layer on 2 baking sheets. Bake until tender and pliable but not brown, 10 to 15 minutes. Line the side of a 9-inch pie plate with overlapping potato slices so they stick out above the rim; line the bottom with the remaining slices.
Whisk the eggs and egg yolks, half-and-half, chives, nutmeg, 1/2 teaspoon salt, and pepper to taste in a bowl; stir in 1 cup cheese. Pour into the potato-lined pie plate and scatter the remaining 1/2 cup cheese on top. Reduce the oven temperature to 350 degrees F and bake the quiche until just set in the center, 40 to 50 minutes. Let cool at least 20 minutes before slicing.
Photograph by Anna Williams
Recipe courtesy Food Network Magazine