Tie cinnamon stick, cloves, peppercorns, and cardamom seeds in a small piece of cheesecloth; set aside. Fill a large saucepan with 4 quarts water and 1 tablespoon salt and bring to a boil over high heat. Stir in rice and spice sachet. Cook, uncovered, stirring occasionally, until rice is tender, about 10 minutes. Discard sachet and strain rice through a fine-mesh sieve. Let stand in sieve 10 minutes.
Meanwhile, peel potatoes and slice about 1/8 inch thick using a mandoline. Melt butter in a 12-inch nonstick skillet over medium heat, swirling to coat. Transfer butter to a large bowl for the rice mixture. Arrange potatoes in two layers in skillet in a circular pattern, overlapping slightly and working from the outside.
Toss rice with butter, apricots, and raisins, and season with salt.
Sprinkle cilantro over potatoes, and top with half of rice mixture, pressing down to form an even layer. Top with remaining rice mixture, continuing to press down, ensuring rice forms an even layer. Place a piece of cheesecloth directly on surface of rice, covering completely.
Cover pan, and cook for 8 minutes. Reduce heat to medium-low, and cook until potatoes are crisp and golden brown around edges, 20 to 25 minutes. Remove cheesecloth. Run a rubber spatula around edge of pan, and invert onto a serving platter, shaking gently to loosen rice from pan.