Heat olive oil in a large soup pot over medium-high heat and sauté carrots, onions, and celery until softened.
Add diced tomatoes, tomato paste, chicken broth, oregano, and dried basil and bring to a gentle boil.
Cook until the vegetables are tender.
Use an immersion blender or regular blender to puree the soup until smooth and return it to the pot.
In a separate pot, melt butter over medium-low heat and whisk in flour continuously for about 10 minutes until golden.
Ladle a scoop of soup into the roux, whisk to form a paste, and gradually add 2–3 more scoops, whisking until smooth.
Add the roux mixture back into the main soup pot and stir well to combine.
Stir in Parmesan cheese, half and half, salt, pepper, and chopped fresh basil.
Simmer gently until warmed through, then serve.