Preheat your oven to 425°F (220°C). Place the unbaked pie crust into a 9-inch pie plate and gently crimp the edges if desired. Set the prepared crust aside while you work on the filling.
Peel the peaches and slice them into even wedges. Arrange the peach slices inside the pie crust, spreading them evenly across the bottom. Sprinkle the first 1/4 cup of sugar over the peaches to enhance their natural sweetness.
In a medium mixing bowl, whisk together the eggs, milk, remaining sugar, flour, vanilla extract, and optional nutmeg. Continue whisking until the mixture is completely smooth and free of lumps.
Slowly pour the custard mixture over the peaches. Make sure the custard flows evenly between the fruit slices so every bite contains both peaches and creamy filling.
Place the pie in the preheated oven and bake for about 45 to 50 minutes. The custard should be set with only a slight jiggle in the center when the pie is finished baking.
Remove the pie from the oven and place it on a cooling rack. Allow it to cool for at least one hour so the custard can fully set before slicing and serving.