Preheat oven to 375°F (190°C). Heat oil in a skillet over medium heat, add spinach, and cook until wilted, about 2 minutes. Cool, squeeze very dry, and chop roughly.

Whisk eggs, half-and-half, salt, pepper, and nutmeg in a bowl until smooth.

Press pie crust into a 9-inch pie plate. Scatter spinach, then feta and mozzarella over the bottom. Pour egg mixture over top.

Bake on the middle rack for 35 to 40 minutes, until edges are golden and the center wobbles just slightly. Cover crust edges with foil if browning too quickly.

Cool on a wire rack for 10 minutes, then slice and serve warm or at room temperature.