Chop onion and mince garlic. Heat oil in a large saucepan over medium-high. Add onion and garlic; saute 3 minutes or until onion starts to brown. Add tomatoes, broth, oregano, and pasta, in that order. Press with a spoon to submerge the pasta in liquid. Bring to a boil. Cover, reduce heat to medium-low, and cook 7 minutes or until pasta is almost done.
Uncover pan; stir in salt. Add spinach in batches, stirring until the spinach wilts before adding more. Remove pan from heat; let stand 5 minutes. Divide pasta mixture among 4 plates; sprinkle evenly with cheese. Serve with chopped mango.