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.