1. Rinse the rice under cold running water until the water runs clear.
2. Soak rice in cold, salted water for 2 to 3 hours.
4. Bring 4 cups salted water (1 l) to a boil in a medium pot.
5. Add the rice and stir.
6. Boil 4 minutes or until rice is almost cooked.
7. Drain and rinse under warm water.
8. In the same pot, heat the butter and a splash of water until sizzling.
9. In a bowl, stir together only 1/2 cup rice, the yogurt, and the egg.
10. Put it in the pot and let cook for a few seconds.
11. Add the remaining rice and the saffron, in a mound or cone shape (the middle is higher than the sides of the rice pile in the pot).
12. Poke several holes in the rice to the bottom of the pot (the handle of a long wooden spoon works well).
13. Cover the pot with a lid wrapped in a damp kitchen towel or damp paper towels.
14. Cook over medium-high heat for a couple of minutes then lower heat to medium-low and cook for 30 to 35 minutes.
15. Place the bottom of the hot pot in a cold water bath for 30 seconds.
16. Spoon the rice onto a large platter and scrape the bottom of the pot with a metal spatula to release the crust (tahdig).
17. Put chunks of the crust from the bottom of the pot on top of the rice.