In a large skillet over medium-low heat, heat oil. Add onion and cook, stirring occasionally, until softened and translucent, about 7 minutes. Add tomato paste and cook, stirring, until onion is coated, about 1 minute. Continue to cook, stirring, until tomato paste becomes slightly darker red, about 2 minutes.
Add beef, chili powder, garlic powder, and salt. Cook, breaking up beef with a wooden spoon, until browned, about 7 minutes. Add broth and increase heat to high; bring to a boil. Add pasta and reduce heat to medium-low. Cook, stirring occasionally, until most of the liquid is absorbed and pasta is al dente, 10 to 12 minutes.
Remove pan from heat and stir in cheese and yogurt until cheese is melted. Top with chives (if using).