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Bring a large pot of salted water to a boil. Cook the penne until al dente, according to package instructions. Drain and reserve ½ cup of pasta water.
In a large skillet over medium-high heat, add olive oil and the ground beef. Cook until browned and fully cooked, about 6–8 minutes. Drain excess fat.
Push the beef to one side of the pan, then add chopped onion and garlic. Sauté for 2–3 minutes until softened and fragrant.
Stir in the tomato paste and cook for another 1–2 minutes to deepen the flavor.
Pour in the beef broth and stir everything together. Let simmer for 3–5 minutes until slightly thickened.
Lower the heat. Stir in the Greek yogurt and shredded cheese. Mix until creamy and smooth. Add reserved pasta water if needed.
Add the cooked pasta to the sauce. Toss to coat everything evenly.
Taste and adjust with salt and pepper.
Garnish with fresh parsley if desired and serve warm.