Warm olive oil and butter in a large pot over medium heat.
Soften onion, carrot, and celery with a pinch of the salt, stirring, 6–8 minutes.
Stir in garlic, tomato paste, smoked paprika, oregano, and red pepper flakes; cook until fragrant and darkened, 1–2 minutes.
Pour in fire-roasted tomatoes, broth, and sugar. Scrape the pot and bring to a gentle simmer.
Simmer uncovered, stirring occasionally, until vegetables are very tender, 15–20 minutes.
Blend the soup smooth with an immersion blender, or carefully blend in batches until velvety.
Stir in cream, remaining salt, and black pepper. Warm 2 minutes and adjust seasoning to taste.
Ladle into bowls and top with basil and croutons. Serve hot.