Bring a large pot of water to a boil. Rinse 2 cups of rice with cold water and strain. Repeat until the water runs clear.
Stir the rice into the boiling water and add ⅓ cup of salt. Par-cook the rice for 8 minutes. Drain and rinse in cold water.
Separate a cup of the cooked rice into a small bowl. Mix thoroughly with 2-3 tablespoons of Greek yogurt.
Over medium heat, add 3 tbsp butter and a few splashes of olive oil to a cast iron pan. Press the rice-yogurt mixture evenly into the bottom of the pan.
Pour the remaining rice on top of the rice-yogurt mixture and pat to form a slight mound. Use the end of a large spoon to make holes that reach to the bottom of the pan.
Cook the rice for 35 minutes, or until the edges of the bottom layer are nice and brown. To ensure even cooking, rotate the pan every 5 minutes as it cooks.
Once finished cooking, run a spatula around the edges of the pan to unstick any pieces. Place a large plate on top of the pan and flip. Serve warm.