1. For the batter, mix the milk, eggs, vanilla essence and lemon zest with 250g of sugar in a bowl.
2. To make the caramel, pour the remaining sugar in a heavy-bottomed pan, and stir it consistently till it melts and turns golden brown.
Note: You can also add a few cubes of butter to increase the thickness.
3. Pour the caramel into a pudim mould (potuguese pudding cast), and add the batter.
4. Cover the batter with aluminum foil, and put the pudim inside a bain marie (also known as a heated bath utensil) and let it cook for 45 to 55 minutes.
6. To cool it, leave the pudding in room temperature for 30 minutes, and then leave it in the refrigerator for one more hour.
7. Once cooled, pudim de ovos is ready to be served.