In a large bowl, beat eggs until light and fluffy. Add rice, ricotta, sugar, orange rind, lemon zest, cinnamon, and vanilla extract. Mix until thoroughly combined.
Roll out half of pastry to fit 24cm deep-dish pie tin. Place pastry in tin, and fill with ricotta mixture. Roll out remaining pastry and cut 12 2.5cm 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.