Cook the rice in boiling salted water for 5 minutes, not more than that. There will be a bite when tested. Drain immediately and pour cold water to stop cooking.
Wash the dill leaves well and drain. Mix in 1/2 tsp salt.
Add into the prepared rice and toss well to spread around.
Cut the potatoes into thin roundrels and set aside.
Heat a saucepan. Melt half the butter and pour in half the saffron water. Spread the potatoes on it. This process is the "tahdig".
Spread the rice over it. Make around five holes around for steam to pass. Cover the lid with kitchen towel and close tight.
Keep on meduim-low flame for 10 minutes.
Melt the remaining butter and mix into the remaining saffron water. Open the lid and pour this over the rice. Keep the flame to the lowest possible flame and cook for 45 minutes.
While serving, toss up the rice together or serve the rice and tahdig separately.