Wash the rice thoroughly, then place in a large pot with 3 tablespoons of the salt and enough cold water to cover by 2 inches. Let soak for 2 to 3 hours.
Drain well in a fine sieve. In the same pot, bring 4 quarts of water to a vigorous boil. Add the remaining 1 tablespoon salt, then gradually sprinkle in the rice. Stir gently to prevent sticking, and bring back to a boil. After the rice has been boiling for 2 minutes, test for doneness. The rice is ready when the outside is tender but there remains a slight uncooked resistance at the core of the grain. If the core of the grain is brittle, it's not done enough. Continue to check the rice until done, usually about 4 minutes, then drain in the sieve and rinse with tepid to cool water (to prevent cooking any more).
Place the pot back over high heat and add the oil or butter and 1 tablespoon water. In a small bowl, whisk together the yogurt and egg. Stir in about 1/2 cup rice, then place in the sizzling oil and spread over the bottom of the pot. Gradually add the remaining rice, sprinkling it in to form a mound. Use the handle of a wooden spoon to make three or four holes through the mound to the bottom, then cover the pot with a lid wrapped in a tea towel. (The towel helps seal the lid and absorbs moisture from the rising steam.) Heat over medium-high heat until steam builds up, 1 to 2 minutes, then lower heat to medium-low and cook for about 30 minutes. When it is done, the rice will be tender and fluffy with a flavorful crust, the tahdig, on the bottom.
The tahdig comes off more easily if, before removing the lid, you place the pot in an inch of cold water (in the sink) for a minute. Then remove the lid and, if you're using saffron, gently spoon about 1 cup rice into the saffron water mixture; stir to blend. Mound the remaining rice on a platter. Sprinkle on the saffron rice, if you have it. Place chunks of the crust on top or on a separate plate; it's a big treat.
Courtesy of Seductions of Rice by Jeffrey Alford and Naomi Duguid