In a large mixing bowl, beat eggs and sugar together. Stir in milk and vanilla.
Arrange peach slices in bottom of pastry-lined pie pan.
Pour custard mixture over peaches.
Bake in preheated oven for 10 minutes. Reduce heat to 350 degrees F (175 degrees C) and bake an additional 45 minutes, until custard is set and toothpick inserted in center comes out clean.