Special equipment: an 8-inch non-stick skillet with lid
Rinse the rice until the water runs clear. Cover the rice with cool water and soak for 30 minutes to 1 hour, then drain.
Bring 4 quarts of water to a boil. Add the turmeric and heavily salt the water (it should taste like sea water). Add the rice and boil for 5 to 7 minutes, until the rice is al dente. Drain and rinse with cold water to stop the cooking.
Stir together the yogurt, 3 scallions and 1 cup of the parboiled rice in a medium bowl.
Wrap the lid of an 8-inch nonstick skillet with a kitchen towel, ying the loose ends around lid handle to secure. (This will trap the steam and absorb condensation as the rice cooks.)
Add the oil and butter to an 8-inch nonstick skillet over medium-high heat. Once the butter melts, pack the rice-scallion mixture evenly into the bottom of the pan then mound the remaining rice on top. Use a skewer or the handle of a wooden spoon to make 4 holes to vent the steam around the perimeter about 2-inches in from the outer edge. Make a fifth hole in the center. Cook, uncovered, rotating the skillet halfway through, until the bottom is golden, 6 to 8 minutes. Reduce the heat to low. Cover the skillet with the towel-lined lid and continue to cook, rotating the pan about a quarter turn every 10 minutes, until the rice is steamed and fluffy, about 35 to 40 minutes.
Remove the lid, dig a hole about 1-inch deep in the center of the rice, just large enough to hold the egg yolks, and pour them in. Then cover with the displaced rice. Return the lid to the skillet and cook until the yolk is just starts to set but is still runny, about 1 minute more.
Remove the lid. Use a butter knife or a small offset spatula to loosen the rice from the edge of the skillet. Place a plate over the skillet and flip the crisped rice pancake onto the plate. Sprinkle with remaining 2 scallions and slice into wedges.
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