In a large bowl, beat eggs until light and fluffy. Add rice, ricotta, sugar, orange rind, lemon rind, cinnamon, and vanilla extract. Mix until thoroughly combined.
Roll out half of pastry to fit 10 inch deep-dish pie pan. Place pastry in pan, and fill with ricotta mixture. Roll out remaining pastry and cut 12 1-inch wide strips. Lay strips in a lattice pattern on top of filling. Brush pastry with milk.
Bake in preheated oven for 1 hour, until toothpick inserted in filling comes out clean.