Heat oil in a large heavy-bottomed pot over medium-high heat. Add ground beef; cook, stirring occasionally and breaking up the beef, until browned, about 5 minutes. Stir in carrots, celery and onion; cook, stirring often, until starting to soften, about 3 minutes. Add garlic; cook, stirring constantly, until fragrant, about 1 minute. Add ½ cup chopped basil, Italian seasoning, salt and pepper; stir to combine.
Stir in broth, kidney beans, cannellini beans, diced tomatoes and tomato sauce. Bring to a simmer over medium-high heat. Stir in pasta; cover and reduce heat to medium-low. Cook until the pasta is tender, 12 to 14 minutes.
Divide the soup among 8 soup bowls. Top with Pecorino Romano and the remaining ¼ cup basil leaves.
