First soak your rice and strain it in a metal wire mesh collander, this will get out the extra starch. Do this a few a times until the water is no longer cloudy when you soak the rice.
Boil about 5 Cups of water in a large pot (think wide and deep...omg yikes sorry in advance for that imagery!)
Once the water is boiling, add your rice to the boiling water. As soon as the rice grains elongate and taste al-dente, or as my mom says "al donte", pour the rice into a wire mesh colander allowing the water to strain out. You need to act fast here.
Quickly rub the cooking oil in the pot you were cooking the rice in so it coats the bottom of the pot well. Then add your sliced potatoes so that each potato covers the bottom of the pot, do not stack them on top of each other.
Have the heat set at low (2 if you have a numeric setting for heat on your stove)
Then add your rice back into the pot, add your saffron at this point if you've made it. Stir the top of the rice a little to allow some of the steam to escape. Then add your butter and salt, breaking up the butter into little pieces allows it to spread a little more evenly.
Now comes the hardest part, the waiting. Wrap the lid to your pot in a clean towel and place the lid on the pot. The purpose of the towel is to catch the steam, which will prevent your rice from becoming mushy.
Now just wait, wait longer, the longer you wait at this low low heat the crispier and thicker the tahdig will be (at least 30 minutes typically, probably longer though). You have to really play this by ear. You will either not wait long enough or you'll burn it on your first few trys. It's okay, everyone has burned it before. But by using lower heat you are mitigating the burning risk, it just takes longer to cook.
Once the tahdig is nice and crispy, spoon out your rice first then use a spatula to get the tahdig out.
Enjoy!