Rinse the rice in cold water 2-3 times, or until the water runs clear. Drain and set aside.
Make saffron water by combining ground saffron with boiling water in a small bowl. Set aside to steep.
Bring a large pot of water to boil and add 1 tbsp of salt. Stir to dissolve salt, then add rice and cook for about 5 minutes. Test the texture of the rice between your fingers. The grains should be soft on the edges but still firm in the middle - not fully cooked through. Drain and rinse with cool water to stop the cooking process. Drain rice completely and set aside.
Drain your potatoes and rinse any residual starch off. Shake off excess water, then pat dry with a towel or paper towel and set aside.
Heat the oil and 1 tbsp of butter in a large non-stick pan over medium heat. When butter melts, add 1 tbsp of the saffron water (the water may sputter - be careful not to burn yourself!).
Add the dry potatoes to the pan in a single flat layer and season with a little salt. Layer the partially cooked rice on top, pressing down on the rice gently to pack it down. Pour 1 tbsp of saffron water over the rice.
Poke shallow holes into the rice and push in pats of butter, then smooth the top of the rice again.
Place a clean kitchen towel or paper towel on top of the pan, cover with a lid, and wrap the excess towel around the lid. Be careful not to catch your towel on fire - especially if you are using a gas stove!
Cook the rice on medium heat for 5 minutes, then reduce heat to medium-low for about 20 minutes. Lift the lid to check on the doneness of the potatoes and make sure they are not burning. Continue cooking for another 10 minutes or as needed. The dish is done with the potatoes are cooked through and crispy, and the rice at the top is also cooked through.
Take the pan off the heat and remove the lid. Allow to cool briefly, then cover the pan with a large plate or serving platter, and carefully invert to serve. Do not do this over your stove! You should flip the dish out of the pan and onto the plate on your counter top.
If using, drain barberries, and combine the remaining 1 tbsp of saffron water. Garnish with the saffron barberry mixture. Serve immediately. This dish has the best texture when fresh. Leftover potatoes will become soggy, however the leftover rice is still good the next day.
Please note that the nutritional information for this recipe is only an estimate, and has been calculated using a plugin.