In a large bowl, whisk together yogurt, garlic, salt, and lemon juice to combine. Refrigerate until ready to use.
In a large pot of salted boiling water, cook pasta until al dente, following timing on package. Drain pasta and allow to cool slightly, about 5 minutes.
While pasta water comes to a boil, heat 1 tablespoon oil in a large stainless steel skillet over medium heat until shimmering. Add pine nuts and cook, stirring often, until golden, 1 to 2 minutes; immediately transfer to small plate to prevent further darkening. Season with a pinch of salt; set aside. Wipe skillet clean.
In now-empty skillet, heat 2 tablespoons oil over medium heat until shimmering. Add onion and cook, stirring occasionally, until softened and just beginning to turn golden, 5 to 7 minutes. Stir in cinnamon, cardamom, allspice, and pepper and cook until fragrant, about 30 seconds. Stir in lamb or beef and salt and cook, stirring occasionally and breaking up meat with wooden spoon, until meat is evenly browned and no pink streaks remain, 8 to 10 minutes.
Add pasta to bowl with yogurt sauce and rapidly toss and mix well to combine. Transfer pasta to a large serving dish. Top with cooked meat and pine nuts. Garnish with parsley and mint. Serve.
