Bring a pot of salted water to a boil. Add the pasta and cook as the label directs. Drain.
Meanwhile, heat the olive oil in a large skillet over medium-high heat. Add the onion and garlic and sauté, stirring occasionally, until the onion is translucent, about 10 minutes.
Add the ground beef and ½ teaspoon each salt and pepper and cook, breaking the meat into small pieces with a wooden spoon, until browned, about 10 minutes. Add the crushed and diced tomatoes and their juices and the basil. Bring to a simmer and cook, stirring occasionally, until slightly reduced, about 15 minutes. Stir in the cheese just before serving.
Divide the pasta among small cups and spoon the sauce over the top. Sprinkle with more cheese.