Rinse the rice thoroughly, by putting it in a bowl, filling the bowl with water, stirring rice around, emptying the water, and repeating the steps a few times. Then fill the bowl with water and let the rice soak for an hour.
Boil ½ cup of water. Grind down the saffron strands with a mortar and pestle, add to the boiling water in a cup, stir and let sit to cool down.
Drain the rice and put in a medium-sized non-stick pot. Add three cups of water, which should come up to about one finger joint above rice level. Add the salt and 1 tbsp oil, place lid and bring to boil. Once it starts boiling, reduce heat to medium, remove lid and let the water evaporate. Once there is hardly any water left, remove from heat, drain in a colander and give it a quick rinse under cold water.
Wash and dry the pot, then drizzle some oil to cover the entire bottom.
Combine 1 tbsp of the melted butter, 1 tbsp oil and 2 tbsp of the saffron mixture in a bowl. Add about 1 cup of the rice and yogurt. Mix well and spread on the bottom of the pot with a small spoon or by hand to create a full layer of the yellow rice mixture. Pat down to slightly compact, then slowly add the rest of the white rice and straighten the mound.
Pour the rest of the saffron mixture around the circumference of the rice, and drizzle 1 tbsp butter on top.
Wrap the pot lid tightly with a dish towel, place the lid and cook on low for about 2 hours. This would be one setting higher than simmer mode.
Remove from heat and let sit for 10 minutes. Then take lid off, place a large plate on top of the pot upside down, hold the plate and pot handles with two hands and flip the rice onto the plate. Use of oven mitts are strongly recommended.