Place 4 cups water in a saucepan over medium-high heat; bring to a boil. Add rice; cook for 10 minutes. Drain. Rinse with cold water; drain.
Combine yogurt, salt, and saffron in a medium bowl. Add rice to yogurt mixture, stirring well.
Melt butter in a medium nonstick sauté pan over medium heat. Add oil; swirl to coat. Add rice mixture to pan, lightly packing rice down. Wrap a clean, dry dish towel around lid to pan, tying it at the handle; place prepared lid on pan. Cook rice, covered, over medium heat 20 minutes (do not stir or uncover). Reduce temperature to medium-low; cook an additional 20 minutes or until rice is tender on top and a golden crust forms on bottom.
Loosen the rice crust with a rubber spatula around the edges. Place a plate over the top of pan, and invert the rice onto plate, browned side up. Cut into 6 wedges, and serve immediately.