Bring a large pot of well-salted water to a boil.
Place the rice in a large bowl, rinse with cold water and drain in a colander until the water runs totally clear. Drain well.
Add the rice to the pot and boil until the grains are soft on the outside but still hard at the center, about 6 minutes. Drain the rice and rinse under cold water.
Measure out 1 1/4 cups of the parcooked rice and transfer to a bowl; stir in the yogurt, the 1 tablespoon melted butter and 1/4 teaspoon salt.
Melt the oil and the remaining 1 tablespoon butter together over medium-low heat in a 2- to 3-quart nonstick pot with a tight-fitting lid. Add the yogurt rice and spread it evenly to cover the bottom of the pot. Add the remaining rice, mounding it into a pyramid shape. Insert the handle of a wooden spoon into the mound 3 or 4 times to make vents for steam to escape. Increase the heat to medium-high and cook until the rice starts to steam, about 2 minutes. Reduce the heat to medium-low and cover the pot, first with a clean towel and then with a lid. Steam until the rice is fully cooked and a golden brown crust has formed on the bottom, about 50 minutes.
Spoon the loose rice onto a platter, then use a firm spatula to remove the crust from the pan. Top the rice with the crust and sprinkle with the parsley and sumac if using. Serve immediately.