Add olive oil to a large soup pot over medium-high heat. Once hot, add carrots, onions, and celery. Sauté for a few minutes until they begin to soften, stirring occasionally to prevent sticking.

Stir in diced tomatoes, tomato paste, chicken broth, oregano, and dried basil. Bring the mixture to a gentle boil and cook until the vegetables are tender, around 20 minutes.

Use an immersion blender or regular blender to puree the soup to your desired consistency. If using a regular blender, work in batches and be cautious as hot liquid can expand.

In a separate pot, melt butter over medium-low heat. Stir in flour, whisking constantly for about 10 minutes until golden brown, forming a roux that will thicken the soup.

Gradually add a ladle of soup to the roux, forming a thick paste. Continue adding soup until smooth. Transfer the roux mixture back to the soup pot and stir to combine.

Stir in parmesan cheese, half and half, salt, pepper, and fresh basil. Adjust seasoning with additional oregano and basil if desired. Cook until warmed through, ensuring the cheese melts completely for a smooth finish.