In a small bowl, soak bulgur wheat in 1 cup water for 30 minutes.
In a food processor fitted with a chopping blade, blend [1/2] of yellow onion and basil for 30 seconds. Add bulgur, and blend for 30 more seconds.
Add ground chuck, 1[1/2] teaspoons salt, black pepper, allspice, coriander, cumin, nutmeg, cloves, cinnamon, and sage, and blend for 1 minutes.
Transfer mixture to a large bowl, and knead for 3 minutes.
In a large pot, combine long-grain rice and remaining 3 cups water, and cook for 30 minutes.
In a medium skillet over medium heat, brown beef for 5 minutes, breaking up chunks with a wooden spoon.
Add remaining [1/2] of yellow onion, extra-virgin olive oil, remaining [1/2] teaspoon salt, pine nuts, and seven spices, and cook for 7 minutes. Set aside to cool.
Whisk Greek yogurt into cooked rice, add garlic and mint, reduce heat to low, and cook for 5 minutes.
Form meat-bulgur mixture into 12 equal-size balls. Create a groove in center of each ball, fill with beef and onion mixture, and seal groove.
Carefully drop balls into yogurt sauce, and cook for 15 minutes. Serve warm.