Heat 2 tablespoons oil in a medium skillet over medium heat; add beef. Cook, stirring until beef is cooked through. Remove from skillet and drain on paper towels.
Heat remaining oil in same skillet; Begin heating water for pasta. Add carrot to skillet, cook, stirring, for 4 minutes. Add broccoli and garlic to skillet, cook, stirring, for 2 minutes longer.
Cook pasta according to package directions. While pasta cooking, add beef broth, basil and cheese to skillet. Stir to combine. Return beef to skillet. Reduce heat and simmer for 4 minutes. Drain pasta. Place in a large serving bowl Top with beef and vegetable mixture.
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