Grind the saffron using a pestle and mortar, sprinkle it on 2-3 ice cubes in a jar or a small bowl. Let them melt completely. This will be your bloomed saffron.
In a bowl, toss the chicken thighs with 2 tablespoons of bloomed saffron, salt, pepper, and lemon juice. Set aside while you prepare the rice.
Rinse the rice a few times with cold water until the water runs clear. Drain.
Fill a large pot about ¾ full with water and bring it to a boil over high heat. Add ½ tablespoon of salt and the rice. Let it come back to a boil, still over high heat, and cook for only 5 minutes. Press a grain of rice between your index finger and thumb, the rice should still be firm in the center. Drain, then rinse very gently with cold water to stop the cooking process.
Transfer half of the parboiled rice to a bowl and gently mix it with the remaining 2 tablespoons of bloomed saffron.
Pour the oil into a 9-inch nonstick skillet (about 3 inches deep) over medium-high heat. Place the chicken in a single layer, smooth side up, and sear for 5 to 8 minutes, until slightly golden. Flip so the smooth side is touching the pan. This way, the side facing the rice is already partly cooked, and no raw chicken touches the rice. The chicken won't be fully cooked at this point; it finishes cooking with the rice. The thighs will shrink as they sear, so if they don't all fit at first, sear them in batches, then return all of them to the pan in a single layer before adding the rice. They'll also release some moisture. Leave it in the pan, as it flavors the rice.
Spoon the saffron rice over the chicken and pat it down tightly with the back of a spoon. Top with the plain rice and pat it down tightly again. Using the handle of a spoon, poke 5 holes in the rice without reaching the bottom of the pan. Cut the butter into smaller pieces and place them on top of the rice.
Wrap the lid in a clean kitchen towel, tying the corners up so they stay away from the heat, and cover the pan tightly. Cook over medium heat for 45 minutes. You should see steam within about 20 minutes, which is a good sign.
Turn off the heat and let the pan sit for 5 to 10 minutes. Place a large platter over the pan and carefully invert it in one confident motion. Serve right away.