Bring water and kosher salt to a boil in a pot; add rice and cook, stirring, for exactly 7 minutes. Drain.
Heat olive oil in a pot over medium-high heat. Cover bottom of pot with 1 layer of potato slices. Sprinkle cumin and salt over potatoes. Cook until potatoes are sizzling, 2 to 3 minutes; top potatoes with rice to form an even layer. Reduce heat to low and place butter slices over rice.
Top pot with a layer of clean paper towels and place lid over towels. Steam until rice is fluffy, about 45 minutes.
Grind saffron threads with a mortar and pestle. Mix crushed saffron with 1 1/2 tablespoons hot water in a large bowl. Add a couple spoonfuls of rice to saffron mixture and stir until rice is yellow.
Spoon remaining rice into a serving bowl, top with saffron rice, and line edges of bowl with potatoes. Garnish with parsley.
