Gather the ingredients. Preheat the oven to 400 F.
In a large bowl, whisk together the flour, salt, and baking powder. Slowly add the olive oil, mixing constantly with the whisk or a fork. Add the milk a tablespoon at a time, continuing to stir until the mixture begins to gather together into a ball.
With clean hands, knead the dough in the bowl just until all of the ingredients are well mixed.
Press the dough evenly into a 9-inch pie plate or quiche dish. Set aside.
In a large skillet or chefs, warm the tablespoon of olive oil over medium-high heat.
Add the chopped garlic and saute for 30 seconds, or until aromatic. Add the mushrooms and saute until they soften and release their juices, about 3 minutes. Continue to saute 2 minutes more, or until most of the liquid released by the mushrooms evaporates.
Add the chopped spinach to the pan (it’s fine if it’s still frozen) and saute until cooked through—about 3 to 5 minutes. Remove the pan from the heat and set aside.
In a large bowl, whisk together the eggs and milk. Add a spoonful of the mushroom and spinach mixture, whisking constantly to temper the eggs .Slowly add the rest of the vegetable mixture while stirring continuously. Whisk in the nutmeg.
Sprinkle the vegetable mixture evenly with the flour while continuing to stir until any lumps of flour disappear. Fold in the crumbled feta.
Pour the spinach and feta mixture into the prepared crust. Bake in the preheated oven for 40 to 45 minutes, or until the pie filling is puffed, firm, and golden, and a tester inserted in the center comes out clean.
Allow the pie to rest for about 5 minutes before cutting. Serve warm or at room temperature. Enjoy