Rinse the rice. Place the rice in a large bowl and cover with cold water. Swirl gently with your hands. Strain into a fine mesh strainer. Repeat this process until the water is mostly clear when swirling. This can take up to 8 rinses. Strain the rice and set aside.
Sautée the garlic. Place a large pot over medium heat and add the butter. When the butter is melted, add the garlic cloves. Cook while stirring often until lightly golden, about 3 to 4 minutes.
Add 1 gallon of water to the pot. Now add the salt and bay leaf. Place the burner on high heat and bring the water to a boil. Add the rice and cook while stirring every minute or so until the rice is just tender. This will take 8 to 10 minutes.
Pour the cooked rice into a fine mesh strainer and rinse with cold water until the rice is chilled. Let the rice drain thoroughly. Remove the garlic cloves and bayleaf and discard.
Scoop out 1 cup of the drained cooked rice. Add it to a bowl. Add the yogurt to the rice and fold until thoroughly combined.
Heat a 8 to 10 inch well seasoned cast iron pan or heavy bottomed non-stick skillet over medium heat. Add the duck fat. Once the fat starts to shimmer, add the yogurt and rice mixture to the pan. Flatten out into an even layer so that it completely covers the bottom of the pan.
Add the remaining rice to the pan in an even layer. Gently press the rice down with a spatula. The rice should look neatly nestled into the pan in an even layer. With the handle of a dinner fork, poke about 6 to 8 holes into the rice. This will let steam escape and help with achieving a crispy bottom layer of rice.
Cook for about 15 minutes while giving the pan a gentle shake every 2 or 3 minutes. You're looking for the edges to begin lightly browning.
Lower the heat to low heat and cook for about 20 more minutes.
Remove from the heat and let cool for 15 minutes. Use your spatula to losen the edges of the rice from the pan.
Time to remove the rice. Place a large plate over top of the skillet. With one hand, firmly press the plate into the skillet. With the other hand grab the handle of the skillet. In a smooth fast motion, flip the pan over while still firmly pressing the plate onto the skillet.
If your rice doesn't all come out in one uniform piece, just scrape it off the bottom of the pan. It will still be just as delicious.