Make the dough: In a stand mixer fitted with the dough hook attachment, combine the flour, water, olive oil, and salt. Mix on medium speed until a smooth dough forms, then wrap the dough ball in plastic and let rest at room temperature while you make the filling.

Make the filling: Wash the greens well. In a large pot, bring a few inches of water to a boil. When the water is boiling, add the greens and cook until they wilt, about 2 minutes. (Depending on the size of your pot, you may need to do this in batches.) Transfer the wilted greens to a colander and let cool. When cool enough to handle, grab handfuls and squeeze firmly over the sink to remove as much liquid as possible. Transfer to the bowl of a food processor.

Add the eggs: cheese, olive oil, salt, and nutmeg to the food processor and pulse until the greens are finely chopped and the mixture is well combined.

Preheat the oven to 375°F: Transfer the dough to a floured work surface and cut into two pieces, one slightly larger than the other. With a rolling pin, roll the larger piece of dough into a circle about 12 inches in diameter and transfer to a 10-inch round cast-iron frying pan or ceramic pie plate, leaving the overhang. Add the filling, smoothing it into an even layer. Roll the second piece of dough into a 10-inch circle and use it to top the pie. Pull the overhanging dough over the top piece of dough to seal, then cut a few steam vents in the top crust with the tip of a sharp knife or a pair of scissors.

Brush the top of the pie with olive oil, sprinkle with salt, and bake until golden brown, about 1 hour.

Remove from the oven, let cool slightly, then cut into wedges. Serve warm.